You don't normally prune a Lilac unless it is getting t obit for the space you have.

Which variety of Lilac, the ordinary tree like one or one of the smaller varieties such as Palibin? if its one of the smaller ones, then prune as the flowers finish if you're reshaping or keeping it in check. If its the big tree like one that produces suckers, (one of the Syringia vulgaris types) you can prune now if you want, but it tends to encourage more sucker growth.

It's the normal variety and has a branch that somehow has come away from main shrub and is overhanging on the grass and stopping sun getting to plants next to it. Could I just cut it off?

Oh yes, of course - take it as low down as possible.