16:13-15 What does it mean that the Lord had opened Lydia's heart to receive the gospel?

This does not teach that God had predestined Lydia for salvation, as some claim. Lydia was already committed to the way of God, so "whose heart the Lord opened" simply means, "whose heart was open to the Lord".

Because Lydia already worshipped God, the way had been prepared in her to receive the gospel the same as Cornelius and his household received it in Ac 10 (CP 10:1-6, 21-27, 34-48).