Don't have actual experience with lined 3way ball valves but here is a list of manufacturer's I have for lined ball valves. Maybe you can check with them if you haven't already.
Durco/Atomac
ITT/Richter
Neotecha
Xomox/Tufline
I notice that Atomac (part of Flowserve) lists a model AMP3 3-way lined ball valve.
I think there are lot of Manufacturers, of course... but if you're looking for small diameters (up to 3", stainless steel valves also for "clean" services (food and beverage, pharmaceutical, etc.), you can visit, for example: