Perhaps Lactuca canadensis? This page also covers Lactuca biennis and Lactuca serriola, with copious details and maps for each species: http://www.florafinder.com/Species/Lactuca_canadensis.php If your blooms, pay attention to the flower color, as that varies among the wild lettuces. [Mind you, I won't swear it isn't some other species entirely!]

That is a coontie, a florida native and member of the cycad family. They are very tough and can take a fairly wide range of growing conditions. Once established they are drought tolerant and need little to no care. Moving them really depends on the size of the plant. Coonties have tubers that can be fairly small on a young plant to very big on a large well established plant. You should be able to scrape away some of the dirt around the base of the plant to get an idea of the size of the tuber. I would start digging a little way away from the base of the plant and work your way inwards in order to make sure you don't damage the tuber. Here is a link that might be useful: http://www.floridata.com/ref/z/zam_flor.cfm

Thanks downeastmd. I didn't realize that Parlor Palms sent out new plants. Thanks for your help. This is my first true palm and I'm glad that my original ID for this plant was correct.

Well, we've had it here in the Library for nearly 15 years and grew it from a tiny plant. When I throw things out (or just remove them from the general population for care) patrons freak out. They are attached to seeing the same plants! Plus I'm interested to see if I can bring it back (just for the education of it). It's a big building so there's no trouble keeping it isolated from the rest of the plant population, no spreading the mites isn't as big a risk as it would be at home.