There is no shortage of low-profile CPU coolers to choose from, though surprisingly, comparatively few have RGB lighting. The list grows even shorter if sticking to the more popular brands. Thermaltake's new UX100 ARGB stands out in this regard, and is ultra-affordable to boot.
The UX100 ARGB is a low-profile air cooler for AMD and Intel processors, with support for a wide range of sockets. Shaped like a bowl, it measures 120 x 120 x 25 mm (LxWxH). That's just under an inch high.
Thermaltake includes a 120mm fan with nine high airflow blades. The bulk of the heatsink is an aluminum finned design, which sits atop a copper plate. Cooling power is rated at 65W—that's a bit on the low side, so this would not be a good option to pair with a higher end CPU like Intel's Core i9-9900K (95W), or for overclocking.
As for the lighting, there is a ring of 15 LEDs. It supports motherboards that have a 5V addressable RGB header to sync the lighting with your PC—(you can check out an official list of supported motherboards here (PDF).
Thermaltake has not said when the UX100 ARGB will be available to purchase, but I was able to confirm with the company that it will retail for $14.99. That would make it one of the cheapest coolers out there, low profile or otherwise.