The LCD display itself ought to be pretty inoffensive - the voltages are low, the currents are very low, and there is no necessity for fast edges.
The back-lighting can be a problem. Jim Williams of Linear Technology has written a number of application notes of the subject - I've found AN-81, AN-65 and AN-55 on the Linear Technology web-site - which refer to generating kilovolts to drive cold cathode lamps at ten of kiloherz.
He does recommend a resonant inverter (an example of a Baxandall class-B oscillator, thogh Jim Williams calls it a Royer inverter), which minimises the switching transients.
---------- Bill Sloman, Nijmegen