Amber, 27, and 14-year-old Lily-Rose were seen chatting animatedly over a late lunch before heading to Fred Segal together for a fashion fix.
Johnny is believed to have introduced Amber to his children soon after they started dating in late 2012, and the actress is said to have immediately hit it off with both Lily-Rose and her 11-year-old brother Jack.
Amber was casually dressed for the shopping excursion on a long black maxi-skirt, a cream top and khaki jacket. She wore her long hair around her shoulders and chose fresh, natural makeup. Lily-Rose, meanwhile, chose a beige jumper and jeans with a black bag over her shoulder.
Johnny surprised everyone when it emerged that he had popped the question to his Rum Diary co-star Amber on Christmas Eve.
He was previously in a 14-year relationship with Vanessa Paradis, the mother of his two children, but the couple never tied the knot.
Johnny and Vanessa announced their split in June 2012 – and it recently emerged that the French actress had called to wish her former partner "happiness" with his new fiancée.
"There's no drama," a source told US Weekly. "Vanessa wished him happiness. She's not bitter, she's happy."