Sorry guys, I don't have an Apple earbud to compare these to. I do, however, have my girlfriends Apple Earpods.
I'll do this in a "Shoot-out" style format, as it will be easier for the readers to gauge how it will fit into their own sound preferences.
Obviously, this is all subjective, and my opinion.
Lyra vs Apple Earpod:
The Apple Earpod sounds more "V-shaped", far less balanced. Due to its lower weight, the Earpod is more comfortable, though not by much. The Earpod is made from noticeably cheaper materials.
The Lyra sounds far more natural, and to my ears, has a less fatiguing signature than the Earpod.
Lyra vs Yuin PK3:
The Yuin PK3 has more air to its signature, and a lot more treble energy. It's a little peaky around 7-8k, which is usually not a problem, but really stands out when comparing it to a darker bud like the Lyra.
The Lyra has more bass and sub-bass presence, and a slightly smaller sound-stage. The Yuin is more comfortable, lightweight, and less prone to falling out of the ears.
Overall, the Lyra has a more balanced, albeit darker sound.
Lyra vs HiSoundAudio Living:
The Lyra is the more comfortable of the two, and has a more balanced signature again. The HiSoundAudio buds are a little difficult to compare to, due to their large size. The Living earbuds definitely had a sharper "V" shape to their sound, with a lot more treble energy. The Lyra was easier to get a good fit.
A darker, more realistic and "natural" signature. Loves to be used at a "realistic" volume setting. In terms of sound alone, it's one of the better earbuds I've heard, for my tastes. The build and materials are fantastic and high quality, but lead to a slightly higher weight, which can cause some discomfort over time. I can't personally use them for workouts, as they will fall out of my ears.
They came with a solid metal tin, over ear hooks, and a variety of different black socks.