I haven't gotten into them yet, but it is quite possible that LED lamps use some sort of switching power supply which can be far more efficient than a dropping resistor. One of the reasons dimmers can be problematic is that some chop up the normal AC sine wave into weird chunks that play havoc with the internals of electronic gizmos down the line. A friend claims he got some CFLs that will operate on a dimmer -- but they were $20 apiece vs the usual buck or two.

I wouldn't expect problems from relays; they are just a switch that uses a magnet instead of a finger to flip the contacts.