1934, actually... and, this is going to ruffle a few feathers, the Lions didn't invent Football on Turkey Day. They weren't even the first NFL team to do it.
What made the Lions effort unique were two things: First was the fact that Lions owner George Richards also owned WJR, which was part of the Blue Network (which became ABC) and the Lions game was broadcast nationwide on the radio. And of course the second thing was that the Lions would go on to do it (almost) every year after. (They didn't play in T-Day during WWII.)
So the Lions didn't invent it, but they were the ones who made it wildly popular and cemented it as a NFL tradition. Lots of the info here was pulled from the wikipedia article on NFL on Thanksgiving Day if you want to read more.
Some numbers (also pulled from there):
The Lions have played 85 T-Day games. Second closest is of course the Cowboys with 58. The Bears and Packers are tied for 3rd place with 38.
Most wins also goes to the Lions with 38 wins. With them also having 46 loses and 2 ties that's a sad .452 WPct. Second place is unsurprisingly the Cowboys with 35 wins.
The Arizona Cardinals have the 5th most T-Day games as they used to host them quite regularly in the past in their various stops around the country. As the Chicago Cards they hosted 1922, '24, '33-'35, and '50. As the St. Louis Cards they hosted on '75 and '77.