There was a LFS Nations Cup, but its organization was flakey for both the league and nation entrants.
Any kind of nations cup will require a damn good league staff, as well as a better system for the racing and nominating of each nation's drivers. The league somewhat leaves out a lot of good potential drivers for a nation, because not everyone can compete all at once, so there needs to be at least 4 or more people interested for each nation.
Hell if there was 30+ nations total in an LFS League, it would be very hard to have all those nations show up and give support. You'd just need to make sure everyone is committed to the league, so there are no fallouts.
And yes, using the FO8 would be ideal, it is the best open wheeler LFS has, and the structure for the league could be exactly like A1GP. The past nations cup that Nikimere ran, he had chosen to use different car/track combos, and that kind of mixed it up too much I think. Sticking to the FO8 could work.
I don't know why someone doesn't start up a new one to be honest, it really would be fun to have such a series again... and actually have it finish. If anyone is thinking of doing it, I could help.