"Full coverage" is a vague term; however, I believe you are referring to "fully covering the motorcycle itself." If that is the case, you are talking about comprehensive and collision coverages.
If you do not have the title to the motorcycle, I believe your lease company will require you carry these two coverages to protect their motorcycle. Also, since it is leased (and not just financed) your lease company may require you carry higher limits of additional coverages like bodily injury liability and property damage liability. Please check with your leasing company to verify this.
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