infinitive or -ing verb
Solution 1:
The form they use in the lyrics is acceptable, and even preferable to the gerund version in this case. There are many cases of of sentences with a noun phrase like all or the only thing followed by a relative clause involving a subject and just do, and then is + a bare verb. We see it in sentences like:
All I do is win
The only thing I could do was watch
So I believe the lyrics in question are preferable as they are.
Note: If you inverted the sides of the word is, then you would need the gerund absolutely, as in:
Bringing you down is the last thing I do