depends on the size of the lake really, a 10 acer lake just needs the anglers to not fish into spawning areas smaller waters might need to close, i'm going to get out at least once more before june they i've thought british carp a few generations in may spawn earlier than they did 20 years back.
my club lake only had me on doing overnight, few other anglers doing the evening. the other big lake hardly had anyone on, had a good look around that, said to be a few fish in there that hardly come out, not surprised there are lakes with in the lake, plot up in the wrong area and you might not even see em.