I've been through the desert on a horse with no name

It felt good to be out of the rain

In the desert you can remember your name

'Cause there ain't no one FOR to give you no pain.

Someone told me that it's hard to find sense in some American songs, which may be true.

Потом погуглил и вроде бы оказалось, что прав: http://en.wiktionary.org/wiki/for_to и http://en.wiktionary.org/wiki/Citations:for_to#English

Вот, к примеру, из американского СМИ. https://triblive.com/local/westmoreland/dewey-bunnell-excited-to-bring-rock-group-america-to-greensburg-on-50th-anniversary-tour/:

"Dewey Bunnell excited to bring rock group America to Greensburg on 50th anniversary tour

...I’m talking about America the folk-rock group, the band that produced hit songs like “Ventura Highway,” “I Need You,” “Tin Man” and of course “A Horse With No Name,” which went to number one on the U.S. Billboard Hot 100 in late 1971".

You're all a good helping bunch.

backward's input clarified a bit more. Looks like it has something to do with the NON-FINITE forms of the Verb (The Infinitive and the Gerund)

"Cause there ain't no one FOR TO GIVE you no pain." = "Cause there ain't no one FOR GIVING you no pain."