'She lives there' is Present tense, which is used to express a fact. When we state a fact, we are not concerned about time. For example, "Gold is very valuable."
Just when it began to be regarded as valuable, and whether the bottom might drop out of the gold market some time in the future, are both irrelevant.
So, if you ask someone, which house does Mary Jones live in?, the person just points and says, "She lives there." That she moved into that house five years ago, or just that morning, is irrelevant; as is, similarly, how much longer she intends to live there.
A Present tense fact thus disregards any idea of being bound by time, some beginning and end.
HOWEVER, that is exactly what the Present Continuous tense does: it indicates that the speaker sees a definite start to the event/action, and that he foresees an end.
So - "I go to that shop rather than go all the way into town to a supermarket" means that that is the shop where I do my grocery shopping. (Fact)
(When I began patronising that shop, and how long or not I might continue to do so is irrelevant.)
BUT: I am going to the shop", in the Present Continuous, indicates the start of the action (leaving the house); that it is happening right now; and will end when I get home.
So - "She is living there..." indicates that this is a temporary state of affairs, as in, "Mary moved in with her aunt. There was a fire at Mary's house, so she is living there until the damage is repaired."
is living: the start was when she moved in with her aunt; it is happening/ongoing right now, but temporary; and will end when Mary moves back into her own home.
"My home is in Liverpool (=I live in Liverpool) but I'm living (am living) here in London while I attend Uni. "