It will, but I don't think you'd be all that happy with the result on such an old unit. Lion should be available in the app store at least until Mountain Lion is released, possibly longer, but no one really knows for sure except maybe a few people at Apple.
I don't know exactly when it is Apple will be releasing 10.8, but you should have at least until then to buy 10.7. I would honestly not be surprised if 10.7 remains available for quite some time after since one of the benefits to digital distribution is that they don't have to pay to keep producing media to ship to retail outlets. The marginal costs of keeping it available for older units that don't make the cut for 10.8 is negligible, and might well make them a small bit of money on the tail end. Even assuming they follow the same basic system they did previously with physical media, they generally always sell the previous and latest version of Mac OS X. When 10.7 came out, they stopped selling 10.5, and so when 10.8 comes out I would expect copies of 10.6 will start to become hard to find at retail. So using that model, you'd have until 10.9 came out to get 10.7, but worst case scenario would probably be that 10.7 goes away the same day 10.8 launches.
And I'll also just add that I wish I could speak a second language even half as fluent as your english. When I went back and looked after seeing your comment, there were a couple of minor things that kind of give you away as a non-native speaker, but honestly you have better english grammar than plenty of native speakers. I'm mildly jealous, as my french never really got past the level of about a toddler, maybe not even quite that.
I have a macbook, but the screen backlight doesn 't work. I'm repairing it, but it may take 15 days till i get the stuff i need to do it. When my macbook works again, i want to upgrade to OS X Lion, but i need to know if mac is compatible and how long Lion will be in the Mac App store. I don't wanna wait for mountain lion because i 've read that my mac can't run mountain lion.
I have a white macbook 2.1 with a 1.83 ghz Core 2 Duo T5600 processor, 2 gb ram and a 60 gb hard disk.
Will my mac be able to run Lion? Now its running Snow Leopard.
And i need to know till when Lion will be downloadable in the Mac app Store, because i'm not going to buy it now, because maybe i can't repair my mac.
Thanks in advance. and sorry for bad english XD