The Bogomolov–Tian–Todorov (BTT) theorem states that smooth Calabi–Yau (CY) varieties over the complex numbers have unobstructed deformation spaces. While this fails over fields of positive characteristic, recent results of Brantner–Taelman and Petrov show that the BTT theorem does hold in positive and mixed characteristics for ordinary CY varieties without crystalline torsion, implying that such varieties are liftable. In this talk, we study the problem of liftability for singular CY surfaces over the ring of Witt vectors W(k). In earlier joint work with Brivio–Kawakami–Witaszek, we proved that normal globally $F$-split CY surfaces admit an equisingular lifting over W(k). Together with Q. Posva, building on the explicit birational geometry and the deformation theory of log CY surfaces, we further generalised this result to the case of globally $F$-split surfaces with semi-log canonical (in particular, not necessarily normal) singularities. In the first part, I will recall the setup and definitions in positive characteristic algebraic geometry, giving an overview of the proofs of some of the previous results. In the second part, I will focus on joint work with Posva and highlight the difficulties that arise in the non-normal case.