"my strengths lie" is a correct and usable phrase in written English. It is typically used to describe one's innate talents or skills. For example, "My strengths lie in mathematics and problem solving.".
"That's where my strengths lie.
"My strengths lie in communication, the building up of the relationship".
Tom Moebus, the school's development director, had sorted through almost two hundred applications for the fifty spots, and he thought the candidates showed an encouraging degree of self-knowledge ("My strengths lie in customer service/support.
"It's gutting because I'm in a really nice position now, but I have to think about where my strengths lie this week and they definitely lie in the speed disciplines.
My strength lies in attack.
My strength lies in advising CEOs, not being one.
"I was lucky enough to know that my strength lay in my hands, not in my social skills," he writes.
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union