She knows who's the alpha. She is showing her belly to him in total submission. Tank will be fine with her dog. Dog hierarchy is a tricky business.
I (already owned by a schnauzer named Gus) took in Brady when my exhusband passed away. Two alpha dogs just didn't work. They hated each other. So what did we do? Adopted a third top dog, a sheltie named Finn. RRRRRough times in our house!
Brady passed away and Gus and Finn are still battling for top dog status.
But I think you'll be fine with Lili and Tank.