Lex have more damage, but androxus wins on mobility.
Try to strafe/dash in between shots, and use your Q on his RightClick and you should win.
This is a skill match up.
Your ult is arguably worth much less than vivians ult in the long run, so letting her keep the drones up is a bad idea. If you have your ult when you hear her pull out her drones, seek her out and use your ultimate to kill her and her drones quickly.
If the tip of his arrow shimmers, he is preparing an Impaler Arrow. Avoid being pinned to the wall at all costs; his Planted will do 2400 damage before you can even move again, and likely another 2400 to follow, killing anyone.