Male lions kill cubs as part of their natural lifecycle. When a new male lion takes over a pride, by killing or driving away the former leader, it will kill all cubs. I don't think lionesses are very successful at preventing this.
From Wikipedia (article: Lion):
"When one or more new males oust the previous males associated with a pride, the victors often kill any existing young cubs, perhaps because females do not become fertile and receptive until their cubs mature or die. Females often fiercely defend their cubs from a usurping male but are rarely successful unless a group of three or four mothers within a pride join forces against the male."
What you say is true however: lions won't select other adult lions as their prey, for obvious reasons.