The controller on our character modules is well within operating range at 3.3v, so that's no problem.
For 3.3v operation of the LCD screen itself, you'll want to pick an LCD with the negative voltage on board, and use the generated voltage from that pin to assist with driving the display, using a 10k pot.
A typical character LCD (such as the CFAH1602B-YYH-JPV needs to have a Vlcd of 3.8-5.2v. If you have the LCD driven from a +3.3v supply, then that means pin 3 (Vo) must be set in the range of -0.5 to -2.9v.
If you have one of our "-V" suffix displays, (negative voltage generator on board), then the display makes an output of -3.3v on the Vee pin. You can then use this voltage to drive the potentiometer, which gets connected to Vo.
Of course, if you have a negative supply available, you can use that instead of purchasing an LCD with a negative voltage generator on board.