I have more experience with Windows than linux. But I would think the concept is similar.
if the client application is linking dynamically to my application which has itself been built dynamically.
I'm not quite sure if I understand "building dynamically". You might be confused with the dynamic aspect of dll? dll is linked at runtime (not build time) to allow a part of component to be deployed without a full app. For example, an app on Windows that rely on a dll provided by the OS are not impacted when Windows updates that dll as long as the interface is maintained. The only difference between a dll and exe is that dll's entry function is dllmain as opposed to main in exe.
(The only "dynamic build" concept I can think of is building templated classes. But I don't think that's what you mean here.)
Hence, debugging a .dll isn't different from debugging a .exe, it's just that .dll is a separate binary file from the executable. All the source code provide is allowing debugger to align the stepping with lines in source code. When source code is not available, then debugger can still step through assembly code with symbols.
When situation doesn't allow, then developers who are good at reading assembly code can do debugging with only symbols and no source code.
You can usually build a binary with optimized option, then compiler might optimize the assembly code so much that source code alignment in the debugger might not be possible. This usually happens with released code. In those cases when you step through the code, you sometimes see the line or condition jumps that are seemingly different from what you would expect. There is the same on .exe, .exe with libs, or .dll. This is probably why you thought it is always necessary to build your own binary to debug dlls?