Dreaming of lovers' families in a hurry to save themselves has two meanings:
(1) implies that the dreamer has a good relationship with his lover's family, which reflects that they care about you, help you and support you.
(2) If this is an anti-dream, it is a manifestation of repressed desire, suggesting that the dreamer expects to live in harmony with his lover's family, care for and support each other.
Generally speaking, it is auspicious to dream of being rescued, which means everything goes well.
Good luck!