Ryan asked: Am I allowed to ride my moped in a bike lane?
Moped operators are required to keep as far right in the roadway as is practicable. The bike lane is part of the roadway, so using the bike lane seems not only to be permitted but required under some circumstances, but that is not specified as it is for bicyclists. There are many exceptions to the requirement to stay to the right. For all the details see this post:
You may also want to review the information in this post about motorcycles in the bike lane. In particular, see Dwight’s comment about preferential use.