"The Lord is mindful of his own" is not a direct quotation from Scripture. Emily Brent may be thinking of Mendelssohn's oratorio St. Paul, which premiered in 1836; one of the ariosos has this title. (You may hear a children's choir singing it here.) Or she may be thinking of the verse on which the arioso is based: Psalm 115:12:
The LORD hath been mindful of us: he will bless us; he will bless the house of Israel; he will bless the house of Aaron.
"Thou shalt not be afraid for the terror by night" is a quotation from Psalm 91:5.