Do you know any airline company owner who holds ATPL licence and flies one of the company's aircraft occasionally in normal operations just because (s)he likes to do it?
Lauda returned to running his airline, Lauda Air, on his second Formula One retirement in 1985. During his time as airline manager, he was appointed consultant at Ferrari as part of an effort by Montezemolo to rejuvenate the team. After selling his Lauda Air shares to majority partner Austrian Airlines in 1999, he managed the Jaguar Formula One racing team from 2001 to 2002. In late 2003, he started a new airline, Niki. Lauda holds a commercial pilot's licence and from time to time acted as a captain on the flights of his airline. Lauda Air ceased operations in July 2013.
Although not an airline Howard Hughes was a test pilot for some of the Hughes Aircraft planes including the famous XF-11 that he crashed.
I can't find any information on if he ever flew any of the Hughes/Air West planes in a commercial situation or if he had a CPL but its worth mentioning.
After some searching I did find this article which states
The only real job Hughes ever had also came in 1933. He signed on as a co-pilot for American Airways. He applied under the name Charles W. Howard. The ruse was quickly discovered, however, and Hughes resigned.
So it seems he did at least try to be a commercial pilot at some point although this was long before the Hughes/Air West Days.
I forgot about it, but Joe McBryan the owner of Buffalo air a small freight and passenger airline in Canada and the focus of the History Channels show "Ice Pilots NWT" fly's some of the flights for the airline.
It also seems that Willie Walsh the CEO of Aer Lingus and then British Airways was a 737 captain however it does not seem that he held these positions while being a captain.
Collett Everman Woolman one of the founders of Delta Airlines (and eventually the CEO) did fly for them when them when they were a crop dusting business (and legally an airline) but I cant find any info on if he flew passenger or mail flights for them.
Walter Varney the founder of both Continental and United Airlines was an airmail pilot for United at one point (possibly also during passenger operations.
Leon D Cuddeback another founder of United Airlines is credited as flying the first airline flight in the country so I'd say he makes the list.
A Felix duPont one of the founders of Allegheny Airlines (eventually US Airways) was a test pilot for Focker and an aviation enthusiast as well as serving during WWII for the Air Transport Command although it does not seem that he flew commercially. His brother Richard Chichester duPont was also an aviation enthusiast and founder of Allegheny Airlines although its unclear if he ever flew for them he does hold some aviation awards.
You can find a list of US based airlines here and the rest of the world here if you want to continue cross referencing owners who were also possibly pilots. It seems that a lot of the early founders/pioneers in aviation were also founders of airlines.
Niels Sundberg, the founder, owner and CEO of EZ (Sun Air of Scandinavia, a franchisee for British Airways) was also a captain for his airline with over 13,000 hours. He was forced to retire from flying paying passengers at 65 under EU regulations, which he describes as big blow.
The Discovery Channel TV series Flying Wild Alaska included COO Jim Tweto who would fly some flights as well (as I remember, mostly bush plane flights).
King Willem-Alexander of The Netherlands occasionally moonlights as a pilot for KLM. Does that count?
The royal Fokker has just been purchased by Alliance Airlines of Australia and replaced by a B737, I presume king Willem will continue to pilot KLM 737s every now and then.
David Eyerly was a cofounder of Surf Air in California. He was a graduate of Embry-Riddle held multiple ratings, and frequently flew the company's Pilatus PC-12s as PIC.
Bruce Dickinson, Iron Maiden's singer is a qualified Boeing pilot (and a champion fencer). He co-founded Astraeus Airlines, which was a charting and wet/dry leasing company. Bruce flew for them, and when Iron Maiden rented one of their 767s (christened Ed Force One), he flew it.