There are wheels with lugs to hold the tires onto the rims ? if so which ones ? no ego here just interested bystander.
Most Eclipse/Hahn-Eclipse/Hahn reel mower wheels had raised lugs cast into the wheel rim which engaged recesses molded into the rubber tire.
Many Toro reel mowers had wheels with grooves and a lug cast into them to engage matching patterns molded into their respective tire.
These are but just two manufacturers, although there were others, as well.
Please keep in mind that there were many brands and models of reel mowers manufactured over the years, and each manufacturer had their own idea of what was best.
Push reel mowers (hand mowers) often used slip-on tires without lugs of any type.
Like you, we often had to boil tires to make them pliable enough to install them. ....Even with boiling, some tires required help from a big hammer to install and properly seat them.