Can we have Italian or straight checkers? Capturing is obligatory, but regular pieces can only capture forwards & Kings can make short movements not ‘fly’.

I've made a post about English / straight checkers before. If loads of online game sites have, I don't see why lidraughts can't. It would help bring a lot of people who only traditionally know that variant (such as us in Ireland) into the universe of draughts.

@ganelon I think its better to add these variants to Lidraughts. Lidraughts is more popular than PlayStrategy

That may be so, but playstrategy has checkers, pool checkers, and spanish draughts and lidraughts doesn't. And their stated mission is to promote international draughts, not to support all draughts variants, so it may not ever happen unless you can code it yourself.

I would love Turkish draughts and Dameo for example but it doesn't seem to be in the works.

Let me state that even Pool draughts on 10x10 board would be a great addition to Lidraughts.
Despite that there is no "maximum capturing" in Pool draughts, Pool draughts on 10x10 board would be more balanced and, I dare to say, more strategic variant than International draughts. While the differences between Brazilian and Pool draughts are not significative to average player, on 10x10 board the differences are essential, because in Pool draughts you will hardly escape from loss by means of two draughtsmen sacrifice at the endgame, if your positional play during middle game was weak. There are dozens of 12-16 draughtsmen positions on 10x10 board which can be won by Pool rules, but which could result only in a draw due to material insufficiency under International rules.