I've come up with a "nice" chorus and worked on the bridge. I also edited the second verse a bit. As for the bridge I'm not quite sure if you can say "single instance" instead of "singular instance". The latter would be correct but quite clumsy to sing. The idea to these lyrics spread from the very first line that kept lingering in my mind until I finally expanded it.
make me your second thought
let's lead our life in sin
grant me the things I sought
but never do me in
keep me under the carpet
and against the odds
avoid the open market
keep out of sight of Gods
let's lead our life in secret
let's take what's been denied
let's avoid the public and
accept what is implied
leading our life in secret
while we feel in line
let me taste your sex
send shivers up my spine
while our bodies flex
let's lead our life in secret
let's take what's been denied
let's avoid the public and
accept what is implied
leading our life in secret
here's our deal today
a climax for a guilty conscience
there's not the lame excuse
of a singular (single?) instance
let's lead our life in secret
let's take what's been denied
let's avoid the public and
accept what is implied
leading our life in secret