I've been working in chemical industry around 15 yrs so far.We have a machineshop at work and guys machines titanium parts daily.I've never heard that titanium will catch fire when machining it either.I am an amateur with lathe,but i've done few small personal projects after working hrs with permission and never started fire either.
Last time when i was messing with titanium,i made these spring holding taps for my shrinker/stretcher:
Only reason for making them from titanium was that i couldnt find any stainless steel from the trashcan,but i found a small piece of titanium bar,so...
Its machines pretty much same way than steel and tig welding it its not hard either,it just requires shielding gas on the opposite side of the piece you are welding.