It's true that coming up with an interface for an abstract debugger is harder, but it's not impossible. Microsoft created Debug Adapter Protocol (https://microsoft.github.io/debug-adapter-protocol/), which is conceptually similar to LSP. It's not perfect, but covers most basic operations pretty well, while leaving to the debugger to deal with the implementation details.
It's true that coming up with an interface for an abstract debugger is harder, but it's not impossible. Microsoft created Debug Adapter Protocol (https://microsoft.github.io/debug-adapter-protocol/), which is conceptually similar to LSP. It's not perfect, but covers most basic operations pretty well, while leaving to the debugger to deal with the implementation details.