By interpreting these lines into modern English language we'll get such an explanation: "There’s still a bit of daylight in the sky. All the late travellers want to get their accommodation quickly". Lated is used in Shakespearean English and means belated here. Belated is another version for lated which means happening later than it should be.
The word 'lated' is 'likely a Shakespearian version of belated'. It is a contraction, a shortened version of the word belated, meaning basically - late.
