*Would putting the CPU back in without using the lever allow the CPU to sit properly?*
This is absolutely NOT the way to remove and refit CPUs.
You may have damaged it - and/or it may be not seated correctly in the socket.
Take off the heatsink and fan - use the lever to remove the CPU (if it actually is inserted. Check the CPU for damaged /bent pins. Clean the old heatsink compound off the CPU and heatsink. Replace the CPU, and push the lever down - refit the heatsink/fan.
Keep your fingers crossed.