Here is the email I received answering some questions I had.
I know quite a bit about Lewmont from that era.
They were a oil well drilling contractor with eight rigs. In about 1980 they sold all of their rigs to Exeter Drilling Northern. Each rig would have a minimum of 21 employees and would operate 24/7. They definitely had at least six and maybe all eight crews out of Gillette. They might have also have had a crew out of Casper or Douglas. Their company yard was in Casper. They had an office in Denver that dealt with finance and marketing.
(1) $58 sounds a little low but it might have been for a single 8 hour shift. A roughneck might have made $7.25 per hour back then.
(2) As with all oil field work, the turnover was pretty high. It was not unheard of for somebody to work only a single day as the work was pretty hard and hiring was done pretty much no questions asked.
(3) In 1979 the oilfield was booming and there were a lot of jobs in nearby coal mines.
(4) I found your site from a Google search on "Lewmont Denver Casper"
(5) Payday was once a week so if somebody worked only one day they would get paid at the end of the week like everyone else.
(6) Sometimes employees would be recommended by others, sometimes not. The work was very hard and more dangerous than most people would be comfortable with.
The company was owned by a guy named Dick Bloss. I'm pretty this is his son. If any payroll records still exist, he might know where they are.