Lex is very usable online. My current ranked record is 309 - 62 with nothing but Lex and maybe 1 or 2 Grundy and Deathstroke. Lex plays very differently from the rest of the cast, so picking him up after playing top tiers will understandably be very difficult and frustrating. However, for this reason I find him to be one of the most fun characters to play. Anyway, first of all online Lex can be a real monster against people who don't know how to play him. Honestly, you can jump 3 spam for wins, and Corp Charge punishes a lot of stuff.
Generally, Lex should be played I'd say anywhere from 80-95% rushdown vs zoning. Lex is all about getting knockdowns to set stuff up or traiting up for armor and more mixups (TRY TO ARMOR AFTER EVERY KNOCKDOWN!). In a close game, d3 is a great footsie tool as are 22d1/22b3, and general starters are f2 (overhead), b13 (low), 22 confirm and 112 (final hits overhead, watch out though as most of the cast can duck 11). A good BnB for online is starter x Grav Pull MB, b3, ji2, 22 x Corp Charge/starter x Grav Pull MB, ji3, 11 x Corp Charge (these are not the max damage but easiest to get off in lag). Also for set up BnB starter x Grav Pull MB, b3, ji2, (22 x close mine/21 x medium mine/u3 x far mine or any of those x probe instead). Probes are important, and in a range game you can probe into orbital. Also orbital MB follows up into another orbital (not entirely true, but a lot get caught by this online. Finally, you can cancel the trait into a dash to lower its ending frames and as long as you are holding circle it will continue to charge. Hope this helps!
EDIT: Oh also Corp Charge wake-up is very invincible and gets a lot of people online.
P.S. I'm actually thinking of creating a Lex Beginner's Guide sometime for anyone coming into this character board similar in style to my stage analysis that will attempt to cover basic things, such as how Lex plays, movement, basic BnB info, how to get to Lex's damage, etc. so lemme know if ya'll think that's a good idea!