I went a bit about the process of redesigning Asterion's lyre here, have you checked it out? I can try and answer any specific questions if you have them.
134 days ago(+2)
They're all based on Greek lyres, though heavily modified from the standard design.
The left one is a chelys-style barbiton. It's by no means a traditional chelys, but still it's chelys-style.
The right one is inspired on the U-shaped lyre from Hagia Triada Sarcophagus while mixing it with the Minoan symbol we call the "horns of consecration." I don't know how I'd classify it, but perhaps the closest would be calling it kithara-style (though not with the movable crossbar that Luthieros has on their kithara model).