Given that lombok's @Wither sticks with the 'withX implies a clone' concept, this is still a pretty bad idea because of the confusion it would add. Builders do not have any methods other than build(), the standard batch you can't avoid from Object.class, and the relevant methods, so the penalty of not having a key word to autocomplete on isn't particularly relevant - and that can be addressed via using @Accessors(prefix = true) (then you get set as a prefix, not with).
The example in link 1 is actually using with as a clone-on-call - it's from jodatime, which uses the same convention as lombok does for what 'with' means: It means clones are being made. Later on in the article, the sentence "method prefix (defaults to with)" crops up, but this is referring to the prefix of clone-with-one-parameter-different methods on immutable classes such as jodatime's DateTime object. This is in fact proof that 'with' is very _inappropriate_ for builder-setters.
The example in link 2 uses an entirely different concept. Here 'with' is the _ENTIRE_ name of the method, obviously it can't be the empty string. This is not setting any kind of convention precedent for how to prefix builder methods. It's also not entirely clear to me if these 'with's are clone-based, or mod-and-return based. I can imagine they are clone based, which would again be further support that 'with' is not appropriate for builder setters.
The major example in the second link is also quite confusing: it's a bunch of with calls, with a random 'skippable()' thrown in, except this seems to either (A) oversimplify things and thus be buggy code, because how can you magically get the best of both worlds and have with() return the Order object when you want that, but return the OrderLine and let you call skippable() on this object when you want that? or (B) it's going overboard on the fluency concept, with Order itself gaining a skippable() method which configures the last added orderline to actually be skippable.
In either case, this example seems sufficiently ill-considered that I'm not sure it should serve as a basis for convention.