I know this could have something to do with the fact that I was sending from a lightning wallet, but I would like to know why the transaction on blockchain.com shows my fee as being ~6.5 sats per byte when I selected 10 sats/byte as I sent the transaction.
Feerates on the Bitcoin network are expressed in sats/vbyte (where vbyte is bytes, but taking the segregated witness discount into account). blockchain.com shows sats/byte (where byte refers to the actual number of bytes used to serialize the transaction); this metric is meaningless for fee estimation purposes.
blockchain.com doesn't show sats/vbyte directly, but you can compute it from the sats/WU that they do show (1 vbyte = 4 WU, so N sats/WU means 4N sats/vbyte).
I recommend using a different block explorer (or none at all; your own wallet will tend to give you more correct interpretations, without needing to trust a single site).