This has been asked before, actually. If I understand what a beat is--and my favorite composers died decades or centuries ago—they are copyright protected, even if not registered. Using them is likely to be a Copr. Infringement, maybe even two. If you re-create the beat it is one, but if you actually copy the beat from a “phonorecord,” then you add infringement of a performance. The only defense I can think of is sincere satirizing of the original song, but that is not what you are planning, is it?
Get (buy) a license or do not do this.
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If you are planning to publicly perform the "beat" with your own lyrics, even without recording the resulting song, this will amount to infringement. As my colleague mentioned, if you are trying to parody or satirize the beat, your performance may protected by the fair use doctrine.
Since you are new at this and need a license, probably two, and you don't know what they are, I suggest you shortcut the process and hire Music Bridge to get your licenses. www.themusicbridge.com
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Interesting question. If the venue where you are playing the beats has a public performance license (ASCAP/BMI), that would seem to cover the playing of the beats recording in the venue. You are then just adding your lyrics, and the resulting live performance is not being fixed in a tangible medium. So you may be alright. You will need to do some further legal research to confirm this. I am curious if my colleagues have any thoughts about this possibility.
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In addition to the other good answers posted here, YES, it is legal so long as you are paying the appropriate royalties. David M. Slater has provided great comments about live performance, as to recording, you will need to cover royalties for both the songwriter and the recording.