Seems to be the imperative-form verb 楽{たの}しめ together with the particle よ.
楽しめ
楽{たの}しむ is the original verb, which means "to enjoy oneself". 楽{たの}しめ, the imperative form, is formed by changing む to め. Imperative-form verbs are blunt, and are used in emergencies, in commands, to be rude, etc.
Thus 楽{たの}しめ roughly means "Enjoy yourself!" (As a command).
よ
The particle よ is often used to soften commands, warnings, insistence, and so on. So it would seem that 楽{たの}しめよ is a firm command, not a threatening one.
In the context of the song, 死{し}ぬまでを 楽{たの}しめよ might be close to "until you die, you'd better enjoy yourself!"
More examples of imperative verbs:
(Father to child:) 早{はや}く 寝{ね}ろ! Go to sleep early!
(Teacher to lazy student:) 勉{べん}強{きょう}しろ! Study!
(Robber to bank receptionist:) 金{かね}を 全{ぜん}部{ぶ}出{だ}せ! Take out all the money! (Caution: かね is a blunt and unsophisticated way to say "money".)