LQG is not believed to allow hypercomputation, i.e. the solving of Turing-uncomputable problems. Penrose's entire argument is based on the idea that the human brain is a hypercomputer, which is why it cannot in principle be simulated by a computer (or any other machine).
It's worth noting that Penrose's field of expertise is General Relativity, not quantum physics, and definitely not Computer Science / philosophy of computation. I see the situation with Penrose as equivalent to Linus Pauling's unfortunate foray into Vitamin C pseudoscience late in his life.