en_tn_lite_do_not_use/2ti/01/05.md

I have been reminded of your

This can be stated in active form. AT: "I also remember your" or "I also recall your" (See: rc://en/ta/man/translate/figs-activepassive)

your genuine faith

"your faith that is real" or "your faith that is sincere"

faith, which lived first in your grandmother Lois and your mother Eunice, and I am convinced that it lives in you also

Paul is speaking of their faith as if it were something that was alive and lived in them. Paul means they have the same sort of faith. This can be stated as a new sentence. AT: "faith. Lois, your grandmother, and Eunice, your mother, first had genuine faith, and I am confident that you have genuine faith as well" (See: rc://en/ta/man/translate/figs-metaphor)

Lois ... Eunice

These are names of women. (See: rc://en/ta/man/translate/translate-names)