This is a copyright issue. Without license or other agreement, it would not be possible to incorporate the lyrics into your logo or other work. This is because you are relying on the intellectual property of another, which you do not have the right to incorporate into your work.
Having said that, I would like to point out that copyright laws vary substantially from country to country. For example, in France, a painting commissioned for the boardroom of a company, but later moved to the cafeteria, could be subjected to restrictions in use.
Also, there are some exceptions to copyright uses. For example, if lyrics were used for satirical purposes, the inclusion of the lyrics might be permissible.
However in the instance you outline, you are trying to incorporate intellectual property of someone else, into your trademark, which you attach to your good, products and image, and in doing so, you would need to obtain the copyright owner's agreement, assuming that the copyright was still valid on the song.
One final note. The song lyrics can be copyrighted, the music can be copyrighted, a performance instance can be copyrighted, and so on. So if you try to secure a license, you will want to be contacting all of the relevant owners.