Is it normal for purpleheart to fade after finishing?

It's the light, not your finish. Purpleheart's purple color comes from compounds in the wood that oxidize when exposed to UV, and it browns out over time pretty much no matter what you do. Direct afternoon sun through a window is basically the worst case scenario, so a couple months of that will absolutely dull it down. Even without sun it happens eventually, just slower. The lacquer didn't cause it and a different finish wouldn't have prevented it. Some people claim water-based finishes with UV inhibitors slow it a bit, but in my experience it only buys you a little time, not a fix. The weird part you noticed actually makes sense. Walnut and cherry go darker with light exposure, so sun is helping them look richer. Maple is pale and low in those light-sensitive compounds, so it barely changes. Purpleheart is the one species that runs backwards and loses its color. All three are just responding to the same window.

For the next one, cut your strips and glue up fast. Freshly cut purpleheart is a vivid purple and it starts dimming within days, so if you mill the stock and then let it sit around for weeks before turning, you're already behind. Sanding right before finishing helps too since fresh scratches expose brighter color, but that's temporary. Other than that, just keep it off the sunny shelf. If you want it to hold purple for display, an interior spot out of direct light is your best bet. Even then expect it to mellow over a year or two. It's kind of accepted among folks who use the stuff that you're borrowing the purple, not owning it. Sounds like you're okay with the brown anyway, which is the right attitude to have with this wood.

Had the same thing happen on a purpleheart accent ring I put in a lamp base a while back. Mine was indoors, no direct sun at all, and it still went dull brown within a year, so I gave up trying to fight it. What I did learn though is a quick sanding brings the purple right back, bright as the day I cut it. Obviously not something you can do on a finished bowl without wrecking the lacquer, but for raw stock or an unfurnished piece it works if you want a fresh pop for photos or a gift. These days I just plan my purpleheart projects around brown.

Funny timing, I just turned a little holder with a stripe of that same purple wood and noticed the shavings coming off the lathe were bright purple, like almost neon. Then the finished piece went dull on me within weeks. So the color really is just sitting near the surface waiting to fade? That kind of blows my mind. Also made me wonder, if I ever make something bigger with it, would slicing the block into thinner pieces and gluing more of them in help keep some color longer, or does it fade the same either way?

Update: moved the bowl off the sunny shelf and sanded the dull spots like the lamp base guy suggested. Purple came right back, so the lacquer was never the problem. I tested a scrap strip near the window too, and within a week it started browning while the shaded one stayed bright. Next one gets a spot away from the glass, brown patches or not.