crt.sh doesn't have any logs: it just aggegrates the certificates submitted to public certificate logs.
Of course Let's Encrypt themselves have a more detailed log, but I'm pretty sure they won't share it with "just anybody" for privacy reasons. But @lestaff can tell you more about that. Perhaps they also can tell us when they do want to share logs and with whom. Might end up to be only law enforcement with the right paperwork, I don't know.
If you're the owner of the domain and you suspect a mis-issuance (i.e., someone managed to get a certificate without the proper authorization), I'm sure Let's Encrypt would like to investigate that. However, if you're not the owner of the domain but just curious, that's almost certainly not enough reason.