Well, not quite at all how you are presenting it.
The US had sanctions in place against Libya going all the way back to 1981. But as you stated earlier, in 2006 both nations were trying to establish ties again so many of the sanctions were lifted. And Vice President Cheney was not in any way "hired" to lift those sanctions, as he was Vice President at the time. That was all part of the effort of President Bush to try and rebuild relations with Libya and other Muslim nations.
But it did not last long, as by 2011 they had become strained yet again, and the Libyan Civil War had the US sever those ties once again.
But it was not just the US, the UN had multiple sanctions against Libya as well. The same goes for Iraq, as US sanctions against that nation came either just before or just after UN sanctions.
Not sure what you mean about "the Stans", as that could cover any of the seven nations that end with those letters. And as many as a dozen others are called that in many languages (especially Turkish), which add "stan" to the end of the names of other nations. Like "Greece", which is called "Yunanistan" in Turkish, Azerbaijani, and Tartar. It literally is just a Turkish and Persian language suffix that means "a Place". And Yunani is the ancient Persian name for Greece. Not unlike say "Germany" and "Deutschland".
Before when Cheney was hired by Halliburton to lobby for lifting sanctions. From 1995_2000. He wasn't VP then. By the Stans I mean those countries that I can't spell that produce gas... like Khazikistan