Why does the law exist?

I'm really not an expert, and i was wondering the same thing. from my understanding, prior to 2008 Luxembourg was like some other countries (like Germany) that nationals could only have one nationality, so you were either Lux or you were not (probably there were some exceptions that certain people got to retain 2 nationalities), so lets say you were a US citizen who went there and decided to become a Lux citizen, in order to become lux you could no longer be a US citizen. These type of policies (one nationality) don't work well for countries that have large immigration populations. This i 'think' was one of the driving forces of changing their nationality law, that portugese, italians, etc nationals that have been living in Luxembourg for a generation (25 years), aren't luxembourgers because they don't want to give up their native nationality. Then these have kids in Luxembourg that normally would be luxembourgers but because the parents don't want the kids to lose their native nationality, they still don't become lux nationals. I think you can see the long term problems you get into with more immigration.
So the solution is to accept dual (actually multiple) nationality, once you've decided that then you need to decide if and how to retroactively apply it, if a luxembourger moved to the US and decided to become a US citizen in 2000, should he be able to reclaim lux nationality? I think most people would agree he should since he was born there and was really his native country.
A lot of countries (especially europe) follow the law of 'Jus sanguinis' where the nationality passes from parent to children, regarless of location.
In my case my father was born and raised in Luxembourg but because he became a Canadian national he lost his Luxembourg nationality, so under 'Jus sanguinis' i would have lux nationality, so the process should be open for me.
The question is how far back do you go - ireland goes back to the grandparents (2 generations), i think Italy does the same. The UK does one generation.
The strange thing about Lux is that they chose an ancestor who had Lux nationality in 1900 - this i don't know where this came from, since you could have 2-3 generations of non-luxembourgish people that still have the right under Article 29 but a person who had possibly a luxembourg parent and grandparent but not an ancestor who had one in 1900 would not qualify.
So to me it is a very weird way to implement a retro-active policy of multiple-nationality.
But that is why the law exists - it is a way of introducing the multiple nationality and being able to re-patriate those who once had the luxembourg nationality and which to reclaim it, where it might have normally being passed down by 'Jus sanguinis'.
i don't recall seeing any official documention about how article 29 came about - so again this is my take on it.

On a bigger scale of why they are doing this, apart from the legal points above, it might be that they want a bigger population and hence more clout in Europe - speculation

From what I read there was a mass exodus of people from Lux to other countries in the late 1800s. Rather than try to maintain their names in the books as citizens it was easier to erase their names. Which stripped many people living abroad of their Lux nationality. This law, I think is supposed to correct that mistake.

I dont remember where I read that however

This sounds too weird to me;
"In the late 1800's to early 1900's there was a mass exodus of people from Luxembourg. From what I was told, the country lost nearly half its population. The authorities at the time freaked out a little because having all these missing people on the records would have become a paperwork nightmare. They made the decision to cross them out and in the process stripped them of their citizenship. The problem being is that they really didn't notify these people or give them a forum to challenge this."

I know there was a large immigration from Lux to the US in the late 19th century (probably more accurate to say large euopean migration to the US), however to me it doesn't make sense that there would be a paperwork nightmare for 'missing' people, and how do you cross them out - out of what - there was no book that said the people listed inside are Lux nationals and if your name is scratched out - you've lost nationality. What i imangine was the condition was that (in 1880-1900) if your father was born in a city in Luxembourg and you were born in 1880 in a city in Lux than you were a luxembourger, now if you hopped on a boat and went to the US, you were still a luxemburger until;
From the law of nationality 1968;
Luxembourg nationality is lost:
1. by the voluntary acquisition of another nationality after age 18;
2. by formal renunciation before a municipal registry officer in the event of
possession of another nationality;
3. by minors whose parents change nationality by the voluntary acquisition of
another nationality;
7. by the automatic loss of Luxembourg nationality in the event of 20 years'
uninterrupted residence abroad of Luxembourg nationals born abroad and
possessing a foreign nationality, unless the person makes a maintenance
declaration every 20 years.

So even if that person in 1900 never took US citizenship (unlikely), their children by taking US nationality (right of birth on US soil - Jus soli) would lose the lux nationality after 20 years, and then certainly by the grandchildren they would have lost nationality by point 1,3 or 7. So by 20 years + 1968 = 1988 there were serveral points on which any Luxembourger that gone elsewhere would have lost their nationality by 1988, fast forward another 20 years and anyone that was a luxemburger in 1880-1900 was either dead or not trying to reclaim Luxembourg nationality in 2008, and any decendants of those people would have certainly lost the lux nationality through the previous laws on nationality.

I suspect more that they considered the most likely longest possible single generation gap - meaning that if a normal generation would be 25 years, so for 1 normal generation gap you have 2 * 25 = 50 years, but you can maximize it to say a generation could be 50 years (less likely but 50 year-old men having children is not as rare these days), so you get a generation gap of 100 years.
Ex - father born in Lux in 1899 - moved to the US - lost nationality - had a child in 1950 - 58 year-old child (2008) wants to regain nationality which he lost but would normally inherited by 'Jus sanguinis' - not because someone discovered he wasn't at home in luxembourg and decided to remove him from the phone book which somehow annuled his nationality.

That story lacks too much details for me, part of it may be true but i can't believe that was the driving force for the law of 2008.

What i would like to know is if there is any historic precidence for this way of doing a nationality reclamation - of just saying any direct ancestor, instead of a more direct parent or grandparent?

From what I can read online, the Lux. government wanted to better integrate its foreigners living in Lux. (Portuguese, etc.) and to avoid having the Lux. citizenship being extinct in a few generations. 

As for why 1900, I remember having read something about it, but I can't find anything. It's a bit weird, as you say. For instance, as for me, my ancestor, thanks to whom I could claim Lux. citizenship, was born in 1821. So, as you can guess, I've never met her, and nobody I've known has. The Lux. link had been really lost. 

I think part of this had to do with trying to " Fix " Luxembourgs " Luxembourgish " population. at one point the majority of the residents in Luxembourg was over 50% non Luxembourgish people. Don't quote me on this as I'm not 100% certain, but I have heard about this somewhere.

Yeah pretty much, but at least it's using people that actually have a bloodline to Luxembourg I guess haha. Either way, I'm glad I have it now.