Nope. They will probably work ok to the naked eye, but you're opening yourself up to other long-term issues.
Stick to one system from one brand. Brands design and test their products to work with only their products. If anything goes wrong, it will be hard to identify exactly which product caused the issue and the brand won't help you as you went against their advice.
You should also only use the lamp recommended by your brand. So you need to stick with the Orly lamp, as it's designed to work with Orly products. Orly won't have tested Light Elegance products with their lamp, so you won't know if the products are curing properly. And just because the look cured, doesn't mean they are