This is made up of two Hebrew names, Li, and Or. The FEMININE form, Liora, is also made up of two Hebrew names, Li, and Ora, the feminine form of Or. Liorit is made up of Hebrew names also. Li, and Orit. Hope this info helps!
The literal translation of this name is "To me a light", but I think it would best be translated to "I have a light". It surely doesn't mean "My light", that would be Ori (also a name). [noted -ed]
Actually, in Hebrew this means "to light" (as in, "from darkness to light" or "I walked towards the light") rather than "my light". The Hebrew prefix "le" or "li" means "to". The Hebrew word "li" means "to me", and would not be used in this context. "My light" in Hebrew would be "Or sheli" or "Ori".
Lior actually does mean 'my light'. Li (lamed yod) means 'mine, my, I have', etc. Just lamed as a prefix means 'to'. So 'to light' is incorrect, while 'my light' is correct.