Can I wire LED light fixtures in parallel?
Based on the Lusa Lighting Model #33000 which are sold under Hampton Bay brand #148652 (For the 3 Bulb White kit), these are not LED lights. They are straight Halogen Light Fixtures.

Each of the Light is a standard 120V Halogen Bulb in a fixture, wired with a standard 2-prong outlet plug. The kit comes with a basic 3 to 1 power strip.

If you have 4 lights, 80W / 120V = 0.667 Amps, you can just use your own power strip instead of the included one. If you have 4 kits of 3, you need up to 12 outlets. Even with 12 20W fixtures, that is still only 240W, or 240W / 120V = 2 Amps.

You could wire them in parallel, but a Power Strip already does this for you, and is safer than wiring it yourself if you are not experienced.

Otherwise see How to connect multiple light fixtures to one switch?