You do not need special cleats for lacrosse, but it helps to wear footwear designed specifically for a sport like it when playing on grass. The sport most closely associated with lacrosse footwear is football, so it has not been uncommon to see players over the last decades wearing low-, mid- or hi-top football cleats on a lacrosse field.
Lacrosse, like football, is a game that relies on speed and lateral movement within a collision sport. Lacrosse-specific footwear, which was not produced until recently, is made to be light, comfortable, stable and offers players maximum lateral traction for cutting and moving.
That being said, weaning cleats designed for other sports like soccer or baseball, is not recommended. In fact, wearing certain spikes, such as metal spikes found on some baseball cleats, are simply not permitted in lacrosse and could result in significant injuries.