Firstly, strlcpy has never been intended as a secure version of strncpy (and strncpy has never been intended as a secure version of strcpy). These two functions are totally unrelated. strncpy is a function that has no relation to C-strings (i.e. null-terminated strings) at all. The fact that it has the str... prefix in its name is just a historical blunder. The history and purpose of strncpy is well-known and well-documented. This is a function created for working with so called “fixed width” strings (not with C-strings) used in some historical versions of Unix file system. Some programmers today get confused by its name and assume that strncpy is somehow supposed to serve as limited-length C-string copying function (a “secure” sibling of strcpy), which in reality is complete nonsense and leads to bad programming practice. C standard library in its current form has no function for limited-length C-string copying whatsoever. This is where strlcpy fits in. strlcpy is indeed a true limited-length copying function created for working with C-strings. strlcpy correctly does everything a limited-length copying function should do. The only criticism one can aim at it is that it is, regretfully, not standard.
Secondly, strncat on the other hand, is indeed a function that works with C-strings and performs a limited-length concatenation (it is indeed a “secure” sibling of strcat). In order to use this function properly the programmer has to take some special care, since the size parameter this function accepts is not really the size of the buffer that receives the result, but rather the size of its remaining part (also, the terminator character is counted implicitly). This could be confusing, since in order to tie that size to the size of the buffer, programmer has to remember to perform some additional calculations, which is often used to criticize the strncat. strlcat takes care of these issues, changing the interface so that no extra calculations are necessary (at least in the calling code). Again, the only basis I see one can criticise this on is that the function is not standard. Also, functions from strcat group is something you won’t see in professional code very often due to the limited usability of the very idea of rescan-based string concatenation.
As for how these functions can lead to security problems… They simply can’t. They can’t lead to security problems in any greater degree than the C language itself can “lead to security problems”. You see, for quite a while there was a strong sentiment out there that C++ language has to move in the direction of developing into some weird flavor of Java. This sentiment sometimes spills into the domain of C language as well, resulting in rather clueless and forced criticism of C language features and the features of C standard library. I suspect that we might be dealing with something like that in this case as well, although I surely hope things are not really that bad.