The Scofield Bible Commentary, by Cyrus Ingerson Scofield, , at sacred-texts.com
Shoshannim, "lilies," and so, the spring; the Shoshannim Psalms were probably connected with the Passover season, and hence reminders of redemption out of bondage, and of the origins of Israel.
This great psalm of the King, with Psalms 46-47, obviously looks forward to the advent in glory. The reference in (Heb 1:8); (Heb 1:9) is not so much to the anointing as an event (Mat 3:16); (Mat 3:17) as to the permanent state of the King.
Compare (Isa 11:1-2).
The divisions are:
(1) The supreme beauty of the King (Psa 45:1); (Psa 45:2);
(2) the coming of the King in glory (Psa 45:3-5); (Rev 19:11-21).
(3) the deity of the King and character of His reign (Psa 45:6); (Psa 45:7); (Heb 1:8); (Heb 1:9); (Isa 11:1-5).
(4) as associated with Him in earthly rule, the queen is presented, (Psa 45:9-13) and in that relation the King is not called Elohim
(See Scofield) - (Gen 1:1)
as in verse 6 (Psa 45:6), but Adonai, the husband name of Deity
(See Scofield) - (Gen 15:2).
(5) the virgin companions of the queen, who would seem to be the Jewish remnant. (See Scofield) - (Rom 11:5). (Rev 14:1-4) are next seen (Psa 45:14); (Psa 45:15); and
(6) the Psalm closes with a reference to the earthly fame of the King.
See Psalm 68, next in order of the Messianic Psalms.