Bilt Hamber is highly rated as a physical clay bar or one of the many Clay Mitts on the market.
Lube - Any weak shampoo mix or QD spray.
In this type of weather it will have started to where off and dirt may begin to bond. You should notice it's not as easy to wash and won't come up quite as clean. If this is the case best to strip it back and re apply rather than top more wax/ sealant over a dirty base. Wash the car as usual then use a tar remover and quick wash again. Then use your preferred polish or cleaner then re wax or seal