The host of Thursday’s event is Red Cavaney, a longtime Washington lobbyist and friend of Mr. Cheney from their days working together in the White House under President Gerald R. Ford. Until Mr. Cavaney retired in 2008, he was the head of American Petroleum Institute, the primary trade group for the oil and gas industry.

Mr. Cheney has become a central figure in his eldest daughter’s campaign. When Ms. Cheney began her bid over the summer, she told associates that she wanted to win in her own right.

But she has plainly recognized what an asset her father can be in a Republican primary. And according to Republicans who have spoken to him, Mr. Cheney, his once-faltering health revived by a new heart, is consumed with helping her win.

He is hosting fund-raisers not just for the new super PAC but also for the campaign itself — he appeared with Ms. Cheney at a finance event in Denver last month.

And Ms. Cheney has not been shy about emphasizing their relationship. In each of her first two ads, she featured images of the former vice president. One of the commercials included one of her daughters referring by name to her famous grandfather.

Last month, when Ms. Cheney and her sister, Mary Cheney, a married lesbian, got into a public argument over same-sex marriage, Mr. Cheney and his wife, Lynne, issued a statement that offered support for Liz’s claim that she had never supported same-sex marriage rights.

As for the super PAC, Liz Cheney cannot, by law, coordinate with the group. But she has family ties with the operative running Cowboy PAC. According to a one-page memo sent along with the invitation, Cowboy PAC will be based in Cheyenne, Wyo, and managed by Barry Bennett.

Mr. Bennett is a Republican operative who has previously worked with Mary Cheney. The organization is still in its nascent stages, though, as the URL on the letterhead simply reads, “This website is currently under construction.”