You do not need to unless your soil is acid, say pH6 and lower, which is unlikely: can you grow blueberries and camelias in your soil? (sign of acidity). My pH is 7.3 and I have never limed.
The manure is fine on top, no need to keep raking it unless there are some large lumps to knock out. Treading on compost and manure when dry is effective at breaking lumps. It is a protective mulch and food for any soil organisms when they are hungry, probably the next time it rains as it is so dry just now. I have hardly touched my soil/compost/manure surface during the last month, to leave all the moisture there, and I notice when pulling some small weeds among garlic and brassicas that there are lots of vegetable roots just below the surface, feeding into my autumnal application of organic matter.