What are the responsibilities of the lead guitarist? Is he the one who is in charge of solos?
A fairly typical setup for a rock band is lead guitar, rhythm guitar, drums and bass. As you indicated, the lead guitarist plays the solo lines, as opposed to the rhythm guitarist who plays chords. It's often the lead vocalist on rhythm guitar, since it's easier to sing while playing chords than while doing lead lines.
However, all of this is completely variable. There are no rules for rock bands. It's possible to have guitarists who trade off on lead and rhythm parts, more than one lead guitarist, or any other combination you can think of.