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!
OK update. That meaning of "Light for me"/"My light" might refer to the BEAM of light that appeared in the universe that came from NOTHING to be "God's gift" -- which can be INTERPOLATED as "Gift of God". It's referring in the way of which God says "Let there be light" -- and then light appeared in the universe. Soooo... The meaning that is "Gift of God" might ACTUALLY be related to that by its light beam. This can also go with the spelling of "Leor".
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.