Well, you can always piece the battings, or get a custom one cut.
But, the largest table for a LA that I'm aware of is 14' (or 168" ). Allow 6" on each side for machine rest/oiling(168 - 12 = 156" ), so 156" is the largest size backing they could accommodate. Length, as you know, is never a problem. This assumes a straight up load, maximum of 156" wide backing, which needs to be 4" larger on all sides of the top (for machine rest/oiling). That makes it 156" - 8" = 148" total quilt top width possible.
148" is the maximum width of a quilt top that they can quilt
Whew...sometimes I go about things the long way :)
Hope this helps.