All of the abbreviations are short for lilies that are interdivisional hybrids. So OT or O/T are short for a cross between an Oriental lily and a trumpet lily. Another term that we toss about for this particular cross is "Orienpet", taking a part of each word from the parents (Oriental and trumpet).
LA is short for the cross between a longiflorum lily and an Asiatic lily. LO is short for a cross between a longiflorum lily and an Oriental lily.
Lilium longiflorum itself is best known as our Easter lily, you know, those lilies with the long white trumpet form that is sold around Easter time.
I know this is all probably somewhat confusing but keep asking questions! I have several books on lilies; one that I like was written by Edward Austin McRae, "Lilies: A Guide for Growers and Collectors". It is out of print now but you can look around for it on ebay or Amazon etc.
A couple of websites that might interest you:
North American Lily Society (aka NALS):
http://www.lilies.org/
The Genus Lilium:
http://www.the-genus-lilium.co...
B&D Lily company has quite a bit of information if you browse around a bit (they refer to LA lilies as "scented Asiatics); two sites:
http://www.bdlilies.com/lilybu...
http://lilybulb.com/f2011.html
Hopes this helps a bit getting you started!