Can a MacBook 2,1 (late 2006) running 10.4 be upgraded to Lion?
You need more RAM and Lion and you are good to go. I linked to one of many providers for RAM that works on your model.



If costs are tight, 2 GB of memory is the minimum requirement for Lion, so that's the only hardware problem assuming your hard drive isn't so full that you can't free up space for the initial install of either Snow Leopard or Lion (you have two paths to get Lion installed).


Get the Lion USB key and hop straight to Lion realizing you will need to erase and migrate things by hand from your backup.
Get a retail Snow Leopard DVD (and optionally the Box Set if you want iLife to be updated but not purchased through the App store). Once you have the updates applied, you can then buy Lion upgrade from the App Store app.


Plan on all your apps not working and you can be surprised if some of them do work. Do make a great backup (bootable one would be best on an external drive) so you can migrate a couple of times or boot and run your old system as you start using the new OS in case you forget some "old documents" or pictures or whatever is missing 3 or 6 months down the road.

Have fun!