The nice thing about T is that it's the first letter of True and of Type. E.g.

  ;; catch-all method for any type
  (defmethod foo ((arg t)) ...)

  ;;
  (defmethod foo (arg ...) ...) ;; alternative spelling: omit class

NIL is the empty list and that is mnemonic for "empty type". For instance, the intersection of two mutually exclusive types is the empty type. Nothing can be both a cons and an atom, so the type denoted by the type expression (and cons atom) is empty; and that is nil. The set manipulation which underlies types needs an empty set, and nil fill the need for that empty set (pun intended).

NULL is useful in writing methods that capture NIL (the only instance of NULL). That may be recognized as the "null object pattern":

  (defmethod foo ((arg null))
    ;; (foo nil) called
    )

  (defmethod foo ((arg number))
    ;; (foo <number>) called
    )

  (defmethod foo ((arg t))
    ;; (foo <anything else>) called
    )