There are multiple origins and meanings for the name:
1. Old French name, comes from the (la mare) meaning - "the pond, sea, ocean"
2. Germanic - "famous throughout the land"
3. Modern Arabic (لمار) possibly "sparkling"or form of the personal name Qamar - "full Moon"
4. Form of the given name Mary - "Theotokos; our lady (Mother of God)"
May also refer to Lamar (male name).