Two changes are needed to have dovecot update lastlog when a user logins with either imap or pop3.

In /etc/dovecot/cond.d/auth-system.conf.ext enable PAM sessions

passdb {
  driver = pam
  args = session=yes dovecot

Then, enable the lastlog module in the dovecot PAM configuration at /etc/pam.d/dovecot by adding the following

session    optional    pam_lastlog.so

Restart dovecot and logins to imap/pop3 should now update lastlog.