Log-liftability conjecture for log del Pezzo pairs with standard coefficients

Work over an algebraically closed field $k$ of characteristic $p>0$. A pair $(X,\Delta)$ is log liftable if it admits the lifting property for the pair and its boundary divisors specified in the paper. Log-liftability conjecture. Assume $p>5$. Let $(X,\Delta)$ be a log del Pezzo pair with standard coefficients. Then $(X,\Delta)$ is log liftable. This conjecture concerns the existence of liftings for log del Pezzo pairs in characteristic greater than five; the authors state that it is open as far as they know.