On the whole it's best to use the one within your chosen system and brand, they'll be tested to work together. I use CND Shellac and Scrubfresh, also CJELP which doesn't need one unless you have problem lifters.
Just to expand on Trinity's comment. Mixing may work, but the chemists only test their complete systems. In the UK, the nail insurance companies who dominate the nail salon insurance market, only provide insurance on the condition that the products are legal but also that the manufacturers instructions are followed. That means potentially that insurance could be invalidated if a complete system, including UV lamp is not used.