Red cabbage work OK? Olive oil since I'm lactose intolerant? Or should I just find another recipe

Visually, red cabbage sometimes bleeds its color over a whole dish.
Taste is fine.
Remember, butter is only about 80% fat, so use less of oil, which is 100% fat, when using it to replacw butter.

Personally I find red cabbage more suited to long braising than green. I think it would work well with the recipe. A good peppery olive oil at the end rather than butter would also be more suited for red cabbage (In my head green cabbage gets butter, red cabbage a vinaigrette and white cabbage is saved for any passing swine that might be peckish.).