So as the manual recommends DOT 3 my car will probably currently have DOT 3 in it, I can still replace what I lose with 5.1 without any complications?
To drain the system - do I simply depress the pedal with the pipes removed until nothing comes out?
Your car will probably have either DOT 4 or DOT 5.1 in it, I think DOT 3 is a bit old to be used these days (though I could be wrong). Yes you can mix 5.1 with what's in there safely.
No, don't just press the brake pedal till nothing comes out, don't let the brake reservoir run dry otherwise you'll get air in the system, and if you get air into the ABS actuator you'll probably end up having to take it to Lexus to get it fixed !
Bleed it a bit at a time, keep topping up the reservoir. Then when you start to see the new clean fluid come through, then you know you've done enough on that one, and move to the next.