There is nothing wrong with the term. I first encountered it in the early 80s, but I think it dates back to the 60s when people started to question the big company profile of the then social contract.
Yiu say, “which is not necessarily the case”. Well in that case it’s not a lifestyle business, as that’s 60% of the definition.
The classic lifestyle business is a surf shop or dive shop: you like the activity, you don’t need a lot of money, you can shut the business for a day (or early) when the weather is good and just go surfing/diving. Some bike shops were like this too, before that business changed.
A consulting business can be like this too. I have friends who are EEs and programmers and they live the same way. One works Jan-march and then takes the rest of the year off unless something is particularly interesting. Another won’t take jobs during ski season. One key is that they love the work (I see comments on HN from people who don’t enjoy programming; for them programming could never be a lifestyle business).
Other businesses like being an electrician can be like this too but for whatever reason don’t get swept under the same rubric.