Congratulations on your great finds, Anthony!
Of course, Lake Tulare is not a martagon at all. It is a complex cross of four western American species. Growing preference will be very different from martagons, but I am betting that the crossings might have made its requirements more forgiving than any individual species. That's why I was excited to see that Faraway Flowers offered it for sale.
Medioloides is from the martagon section of Lilium, and should take similar conditions that L. martagon likes. I would expect that it might not tolerate the heat as easily, and might go dormant quite early. L. distichum (another close relative) does this for me, but without detriment. I have only gotten a hold of L. medioloides seeds last year. They have produce their tiny bulb over the winter, now going through there winter stage, and are slated to be planted out in five days.