LiteSpeed is most useful for sites with very high traffic. Under these conditions, Apache (with typical configurations) would launch many processes in order to handle these requests. Each of these processes would take up some of the cpu time and some of the memory, so even if some of the limits are set higher to allow Apache to "attempt" to handle more requests, that could put other daemons in danger such as mysql, if there isn't enough memory left for them.
LiteSpeed can also help somewhat in a server with many sites of low to medium traffic, if there are enough sites that even this amount of traffic causes high server load. However, in these cases, it may be more effective to split the accounts among more servers.
