Once you buy a game on itch.io, you can download it and any future updates from the project page. If you use the itch.io app, it will work much like Steam where it can apply patches for you automatically, but if you buy and download it via browser you’ll have to redownload the whole game manually whenever there’s an update.
Lancer Tactics saves user data outside of the game folder, so you can delete old versions of the game without losing your mechs/pilots/maps.
We’re planning on bringing LT to Steam later this year, but I’m committed to keeping the itch.io versions up-to-date with whatever versions we release there. I’m hoping we can make steam keys available to whoever buys it on itch beforehand, but as discussed here I’m not 100% on being able to do so, so if Steam is essential for you I recommend you hold off.
Let me know if you have any more questions about it :)