integrating PGP into SMTP.
PGP is a container format for data (like mails but not restricted to mails), which adds encryption and/or signature to the data.
SMTP is a transport protocol.
You don't integrate container formats into transport protocols. This would be the same as saying that you should integrate Office (container for text, images...) with SMTP (transport) to send an office document to somebody.
PGP is also used outside of SMTP, because it is just a container. And SMTP is also used to transport things different from PGP containers, because it is just a transport protocol.
If you instead ask about integrating end-to-end encryption like PGP or S/MIME into SMTP it will not work either, because SMTP is hop-by-hop delivery and not end-to-end. Apart from that SMTP does not even cover the last hop, i.e. the delivery from the last mail server to the client. This is done with protocols like POP or IMAP.
Lea requests the server of Luke's domain jedi.com to tell her the public key of [email protected] ...
That's what you have key servers or other kinds of central directories for. But how does Lea know that this is actually Luke's key and not the key of someone claiming to be Luke? Thus you need to have some trust propagation, for example in the form of a web of trust (PGP) or a more centralized structure (S/MIME) or by trusting everything in a specific central directory.
Thus the task is not to integrate PGP with SMTP but to have better support for PGP in the mail clients, so that they automatically fetch the PGP keys of the recipients. But of course there must be first a verifiable PGP key for the recipient somewhere on a key server or other directory, so the other task is to make key creating, publishing and managing keys (renewing, revoking...) easier. These are all things outside of the mail delivery (SMTP) itself.