I can't be too critical because I often sow different varieties of lettuce thickly in trays for resale. But unless you want to cut baby lettuce greens you should seperate( by pulling apart at roots) and grow in individual cells for a few weeks prior to planting out. Depending somewhat on variety you want to plant 12- 18" apart to get best mature plants.

When and how do I separate these? I want to sow the seedlings into a
raised bed in my hoop house (probably in the next 2-weeks of so).

That looks like a lot of densely sown seedlings! Depends on how much work you want to do. If I was given this tray of seedlings to tackle I'd try to do all the work at once -- meaning rush plant-out time or 'hold' them until you can plant out. In any case, they look about large enough if you want to separate them now. I'd separate something like that by slightly drying the soil, then gently prying out small chunks of seedlings (e.g., a 1" square) -- I use a long slender pickle fork for this! Once you have the small chunk out, you can handle gently to pull or tease individual seedlings apart -- or just plant the small chunk and deal with separating that again later. HTH.

Hopefully it was a leaf lettuce variety rather than a head lettuce type. But wither way I'd use the hunk-o-seedlings transplant method and grow them as leaf lettuce.

Dave

hunk-o-seedlingsthin-and-transplant-at-the-same-time

NICE! Yes the lettuce is a loose leaf type. I really like the "hunk-o-seedling" method.