In general, when working with video (or very large images), lag / performance can be a problem.
The possible solutions vary. Sometimes you have to make the number of patches smaller, but your 55 and 35 numbers sound reasonable.
You may also need to make the pixels-per-patch value smaller. Or you may need to make your particle system create fewer particles, or have each particle move farther in each time step.
There are probably some other ideas I haven't thought of right now, although sometimes there aren't any great solutions.
The lab computers are also probably more powerful than your laptop, and thus may be able to handle creating larger videos.