I know that you know this but lexical_cast was designed to be consistent with {static,const,reinterpret}_cast<Target>(source).
Understood. I do not think though that it might be an issue. The similarity is only cosmetic as the group is supported by the language, works with types when lexical_cast is a library solution, works with values. So, in fact, the user has to learn lexical_cast *not* to use it as the "real" type casts. More so, I'd expect lexical_cast interface extended without interrupting whatever impression/behavior the user has established in relation with the current interface.
It doesn't have to be named lexical_cast. Most likely you're converting from a string, you could name it from_string or something similar.
I indeed often (in 70%) use it for string-to-something conversion. However, for the remaining 30% I need it beyond string-to/from conversion. As for "from_string" I certainly had to do something along the lines for myself. However, beyond my private sandbox I am always reluctant introducing a new vocabulary when the existing can be sensibly reused and (IMHO) improved. Best, V.