It's true that semicolons are normally only used with three or more list items.
However, semicolons are also used to avoid confusion when at least one of the list items already contains a comma.
From The Chicago Manual of Style, 6.60 [paywall]:
When items in a series themselves contain internal punctuation, separating the items with semicolons can aid clarity …
The membership of the international commission was as follows: France, 4; Germany, 5; Great Britain, 1; Italy, 3; United States, 7.
Typically, style is used as a consistent way of preventing ambiguity. If a particular situation calls for something to go against convention, but doing so enhances comprehension, most style guides would allow for its use.
For instance, take the example sentence from Chicago and reduce it to only two list items:
The membership of the international commission was as follows: France, 4; Germany, 5.
The use of the semicolon still aids in comprehension, even though there are only two list items.
Ultimately, it's a matter of personal choice or of what a particular style guide you follow says—assuming it is adamant about not breaking a style rule in any situation.
The following is the sentence in the question:
？ I'm visiting John, my brother; and his wife, Lisa
This is not as clear-cut an example of semicolon use as that from Chicago; however, even if it looks unusual, it's still not possible to confuse the intended meaning of the sentence.
You need to ask yourself if the slight strangeness of the construction is counterbalanced by its comprehension or not.
There are several other ways of punctuating (or rephrasing) the sentence that would be just as comprehensible without the use of a semicolon:
- I'm visiting my brother—John—and his wife, Lisa.
- I'm visiting my brother (John) and his wife (Lisa).
- I'm visiting (1) my brother, John and (2) his wife, Lisa.
- I'm visiting my brother and his wife—John and Lisa, respectively.
In short, the decision to use a semicolon, even if goes against common style guidance, is up to you. I would be hard-pressed, however, to come up with any sentence which could not be restructured or punctuated differently in order to convey the same meaning.