I'm assuming the fish in question is the purple or strawberry pseudo, Pseudochromis porphyreus. I would say there is a good chance both the purple pseudo and the lyretail would harrass the sunburst, a pretty passive fish. This is one of the smaller and less aggressive pseudos but their temper varies depending on the individual and they can attack more passive fish, especially ones added after they have become established. I had a diadema (same genus) that was hell on wheels.
If purple is your thing the orchid pseudo, Pseudochromis fridmani is pricier but even better looking and is very even tempered for a pseudo. You can get captive bred orchids on sale at Drs, from time to time.