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Yes, if there was a signed lease for the time period from 1/2015 to 1/2017 then it would be a valid lease. Your problem, assuming that the current owners dispute whether the lease existed, is proving that there was a written lease. However, if you have extraneous evidence such as emails and texts then most judges will lean toward finding that a written lease existed.
The law requires that any contract for more than a year must be in writing to be enforceable. This is known as the "statute of frauds". However, your issue isn't that it wasn't in writing it is just that the writing has been lost so you have to be sure that the court understands the distinction.
Most judges use their common sense and since you are only talking about 6 more months or so, it's unlikely the judge would throw you out.
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Of course, please feel free to ask any follow up questions in this thread. I want to be sure that all of your questions are answered. In addition, once you issue your Positive Rating the question will lock open and no longer time out so you can come back to it anytime in the future if you think of any follow ups.