The thing is a bit more complicated than you might think. Yeah, lime paint is often the better choice for lime plaster, but not automatically in every case. What really matters is what condition your walls are in. If the old lime plaster is still holding up well and isn't flaking off, then lime paint is perfect - it's breathable and works with the material instead of against it. But if your walls have been painted over multiple times or you've got moisture problems, it gets trickier.
Here's my insider tip: do a simple test beforehand. Grab a putty knife and gently scrape at an inconspicuous spot - if the old paint comes off in chunks and the substrate crumbles, you need a proper primer first before you even think about paint. That'll save you headaches down the road. With walls that old, it's often worth investing in a special deep primer for mineral substrates, regardless of which paint you go with.
Dispersion paint isn't automatically wrong, by the way - just only if the substrate is solid. It adheres better to already-painted surfaces and is easier to work with. Lime paint, on the other hand, you have to mix with water, it smells odd, and it's a bit finicky to apply. But in return, it really lets the wall breathe, which with old buildings is often more important than people realize.