In either case the female is likely to end up with the larger coalition. As long as her cubs are big enough to avoid the new males, she has little to lose. The only risk is that she could get pregnant by a male that is subsequently driven off, only to have her cubs, when they're born, killed by the eventual resident males. With females possibly scheming against them, and rival males always ready to step into their shoes, resident males must be constantly vigilant to keep strange males out of the pride territory. However, if there are cheaper ways to keep intruders out than fighting every one that wanders through, that's even better.
Spoken intentions are notoriously unreliable.
The problem with using words to convey information that must be believed, and with using vocal signals in general, is that they are too easily falsified. Thus to really convince a rival to stay away, a lion should use an assessment signal. After all, owner or not, any lion could proclaim himself one by roaring, and just because he roars doesn't mean that he really will attack an intruder. There are two ways that a conventional signal such as roaring can be made honest. Lions seem to do both.