Good aim will take you a long way on this champion. Learn his range. Always have an escape plan. Understand how to win every matchup (will come with time). Use your mobility!
Furia is strong against Lex from long and short disrance. As long as Furia heals are good Lex wins only with damage shooting from weapon. If she uses her skills reasonably and he'll be catched with beam Lex won't have chances to win solo fight.
Try to place an illusion off to the side of the battlefield to teleport back to if someone, especially someone like Ruckus, starts to target you. This will work even if the illusion expires, but try to keep one hidden from the enemy at all times.
Find where her illusions are and use that to your advantage. If someone targets her, she will likely try to teleport away and confuse you. Surprise her by having someone else near her spot or quickly running after her while staying away from enemies