If you are using low voltage lighting, you need to have access to the "transformer" or power supply.

Take a look at http://www.phantom lighting.com for ideas.

Check out LED tape lighting. SolidApollo even has tape lighting that doesn't require a transformer.

Thew NEC issue is that concealed wiring (inside walls typically) must be an 'approved method' and the 'methods' concentrate on 120 V, 15 A circuits as about the lowest used regularly.
There are a few other 'classes' like power limited control circuits (thermostats fall into part of this group) but they are very power limited.
They might be able to handle an LED strip, but not much else.

120 V wiring has strict rules and every splice must be in a junction box, and accessible (no damage to the finished surface) after installation.
Accessible does not have to be convenient.

The junction box behind a stove is accessible by moving the stove, a panel fastened in pace with screws is accessible, a nailed in place panel is not.

The transformer connections need to be accessible, as well as the transformer itself.

If the wiring is exposed (like on the bottom of a cabinet) and also low voltage you get a lot of relief in wiring methods.