As far as I can tell, the language server protocol and the debug adapter protocol are compatible in how they work. Thus, in my head it felt like a good idea to add some "is_debugging_supported" request, which asks the language server if it also has debugging capabilities. If yes, communication via DAP is also supported, if no, well, one has to find another debug adapter.
By that, reusing the same connection was made easy and some information shall be provided by both, the debug adapter as well as the language server (like goto definition). And thus merging the forces on the server side might be clever anyway.
By that the protocols stay independent but the servers can be implemented with a similar codebase where possible (Mostly scripting languages). The fact that DAP is managed via "capabilities" can even offer a very capable feeling when working with these protocols in combination.
On the client, side when there is support for both, debugging as well as "smart features", both usually are in the same codebase. Thus, it would work here too.