My understanding is that the NixOS Lutris package runs with a virtual FHS that is built with a selection of libraries for running Wine. I think that might mean it doesn't hook up libraries that are configured with nix-ld. If the game runs with steam-app, but not with Lutris, then it sounds like there's a library missing from the Lutris FHS.
You can override to fix that. Looking at the game logs could give you information about which libraries are missing. Or you could add in everything that steam-app uses, the way you configured nix-ld.
There's a configuration snippet that might point you in the right direction in this thread: https://discourse.nixos.org/t/nix-overlay-to-change-fhs-environment/54139/2
