The problem with strlcpy is the return value. You can be burned badly if you are using it to for example pull out a fixed chunk of string from a 10TB memory mapped file, especially if you're pulling out all of the 32 byte chunks from that huge file and you just wanted a function to stick the trailing 0 on the string and handle short reads gracefully.
It's even worse if you are using it because you don't fully trust the input string to be null terminated. Maybe you have reasons to be believe that it will be at least as long as you need, but can't trust that it is a real string. As a function that was theoretically written as "fix" for strncpy it is worse in some fundamental ways. At least strncpy is easy enough to make safe by always over-allocating your buffer by 1 byte and stuffing a 0 in the last byte.
It's even worse if you are using it because you don't fully trust the input string to be null terminated. Maybe you have reasons to be believe that it will be at least as long as you need, but can't trust that it is a real string. As a function that was theoretically written as "fix" for strncpy it is worse in some fundamental ways. At least strncpy is easy enough to make safe by always over-allocating your buffer by 1 byte and stuffing a 0 in the last byte.