.NET 5.0 introduces single file deployments, https://docs.microsoft.com/en-us/dotnet/core/deploying/single-file. The LGPL, https://choosealicense.com/licenses/lgpl-3.0/, section 4 requires that modification to the library be permitted and specifically 4d.1 says:
Use a suitable shared library mechanism for linking with the Library. A suitable mechanism is one that (a) uses at run time a copy of the Library already present on the user's computer system, and (b) will operate properly with a modified version of the Library that is interface-compatible with the Linked Version.
While it may not be easy, and there don't appear to be tools that would permit the library to be swapped out of or replaced in a .NET 5.0 single file deployment, it would seem that this is possible.
Can you use an LGPL library / assembly in a .NET 5.0 single file deployment without violating the license?