In a recent conversation with a native speaker from the Dominican Republic, she used the phrase "llevarle su vida". In the context, I took this to mean "live his/her life for him/her" or be controlling over what the other person did. Is this a correct understanding of the phrase?
This is probably subject to some regional flavor variation, and I'm not very familiar with Dominican Spanish, but here's my guess.
"Llevar" is sometimes used as drive or guide. In this context it could mean to make someone else's decisions.
I.e: I understand "Yo no quería llevarle su vida" approximately as "I didn't want to make his/her choices" or "I didn't want to be responsible for where he/she took his life to".
About llevar with this meaning, it's very usual. As in "llevar a alguien de la mano": take someone by the hand.
My guess is is that she was trying to convey what you guessed in your comment
Yo no quería llevarle la vida I didn't want to interfere in his life; I didn't want to cause him pain.
Your hunch is probably right, since you have most of the context of that conversation.
Nevertheless, the expression
llevarte la vida / llevarte toda la vida
usually means "to take a long time".
Contar todas las estrellas del cielo podría llevarte toda la vida
Estás pintando las paredes con ese pincel tan pequeño? Así va a llevarte toda la vida
Aprender bien takewondo te puede llevar la vida
Juanito está contando los granos de arroz de ese paquete. Le va a llevar la vida
Please, note that this expression id different from "llevar una vida" To life a live (e.g to live a life of excess, llevar una vida de exceso) or "llevársele su vida" Take his life .