Ideas requested – New no-till bed with acidic soil

Hi all – I just built a new no-till bed on top of some existing grass (cardboard + 4-5 inches of compost). I finally got my soil report back and it recommends I add dolomitic lime because my clay soil has a ph of 3.9. I hoped to get the report back before the compost came, but that didn’t happen. How do I do that with the bed? Mix it in? Hoping to begin planting this week. Thank you!