1. The basic answer is that the stereotypical gay lisp and mannerisms are exactly that, a stereotype. In reality, it's a cultural thing that is consciously adopted among certain specific subgroups of gay guys, clustered around the West Coast based fashion and movie industries. Tim Gunn would be a notable example of a prominent, older gay fashion and media figure who exemplifies the pattern and probably contributed significantly to its popularity, although I don't think he's the origin point either.
2. While the lisp and mannerisms are stereotypically associated with gay men, they're not exclusive to gay men. The one person I know who does it naturally -- not as in the over the top stereotype, but as a normal, everyday version of that basic vocal pattern and body language -- is absolutely straight.