Yes, you have a sucker growing off the roots of whatever citrus your meyer lemon was grafted to. All the energy that should be going to support your lemon is being stolen by the sucker - you do need to get rid of it.
The tricky part will be deciding which is the sucker and which is the lemon. I am going to assume it is a dwarf or semi-dwarf Meyer Improved Lemon? Usually, finding the trunk with a graft would tell you which one to keep but the nursery providing these trees prides itself on their ability to graft without leaving a line. Also, lemons have thorns. The rootstock is called C35 Citrus so won't necessarily have the trifoliate leaves either.
My guess would be the trunk that is less vigorous is the trunk you have to keep. If you can carefully dig down at least a couple inches and find where the sucker attaches to the roots and remove it from there, you will have a better chance of keeping it from coming back. If you can't, be prepared to take that sucker out every couple months forever.