Ideally, it is best to mix academic with professional LOR's. However, since you are in a position to only obtain timely professional letters, I would submit two professional letters and one academic - even if the academic is quite old. There are multiple strategies to "refresh" an old professor's memory of your achievements in his/her class. First, submit a packet that includes your resume, transcrips, and personal statement - these materials will guide her/his drafting of the LOR. In many instances, they may even ask you to draft the letter.
In short, more recent letters are best, without question, but try to offset an older academic LOR with a recent professional LOR. You will, however, need at least one academic letter to round out your roster of LOR's.
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