If you are dead set on running the split rims, then you will be fine with a regular tubeless tire. Thousands upon thousands of them have been used with split rims since the tubeless tire took over the market. I am certain there are differences in the beads that the manufacturer can identify but for the average layman, they work fine. I'd be a whole lot more skeptical of a set of 40+ year old split rims than any modern tire you put on them.
Personally, I don't run split rims on anything anymore. After 40-50 years, the machined surfaces that keep the ring on, as well as the metal fatigue in the ring from being taken on and off untold number of times can be reaching the level where a failure is a real possibility. Having grown up around the damn things, I can tell you that we ran them forever but I've seen several of them fail and it's never a pretty thing. Especially under way or if you happen to be standing next to the thing when it comes off. If you are lucky, you get the crap knocked out of you and live to tell about it, still possessing all of your body parts in a functional manner. The options go down hill from there with a dirt nap being at the bottom of the list. Personally, I don't want my kids within 100 feet of a split rim.
As for liners, try looking at 7:00 - 15 TL tire size. That is a heavy duty lowboy type bias split rim tire. You won't like the price. Last one I bought was $40 or more and the valve stem hole might not be in the right spot depending on how your rims are set up. Otherwise, you can get along without a liner, just make sure your wheels don't have any rough spots or sharp edges where the tube will ride. The liner is mainly meant for protecting the tube and keeping it from coming out of the big holes that the lowboy type wheels have for the valve stem. Some of them are 1/2" wide and 2" long. With that style, you have to run a liner.
