Do you know how long ago it was that he had laminitis? Does he currently have any evidence of a problem such as a cresty neck, odd fat pads, or visible ridges/angle changes in his hooves? Does he seem to be shedding out normally? If the laminitis was mild and several years ago and he looks good now while being on a couple hours a day of grass, this is not a situation that would trouble me too much provided you aren't intending on throwing him out on full pasture. If you have the ability to dry lot and manage diet going forward (and are willing to do so), and he is healthy now and doesn't have signs (as Cayuse says, have the vet workup include testing for Cushing's and IR so you know where you're at - IR numbers can go to normal with the right diet, Cushing's needs to be medicated), then it can be very manageable. But of course some cases can be more complicated and it can also worsen with age so that's something you would want to have in the back of your mind.
Every horse and situation is different so it just depends, and it also depends on your tolerance level for what you want to manage or have the ability to manage with your setup, if he did end up needing more than just limitation on grass intake. Are you in the part of WA state where grass grows out of the pavement? From your description it sounds like this is a pretty simple case that dry-lotting would take care of but you can't know for sure until you see bloodwork. These horses DO need owners who are willing to do what is needed for them. So I encourage you because I wouldn't hesitate to take on a horse with this history, assuming I was in a position to provide the living conditions he needed, but I can completely see the other side of it too.