My bluetooth headphones feature the APT-X Low Latency codec, but I tried them with the Miccus Home RTX Mini and I'm still experiencing lip sync delay.

The Miccus Home RTX Mini features the following 3 Bluetooth codecs: SBC, APT-X, and APT-X Low Latency. Your headphones have likely paired to the Home RTX Mini in SBC or APT-X. As per your device specific owner's manual, reset your headphones and make sure they are fully charged. Do a "Factory Reset" on the Home RTX Mini (owner's manual page 10), then pair the RTX Mini and your headphones for use. Click here to link to the Home RTX Mini Owner's Manual.