Invéntame comes from the verb inventar, meaning 'to invent' or 'to create'. In this song, it's used in the imperative form, directly asking someone to 'invent me'.
This word is particularly striking because it's used in a very metaphorical and dramatic way. The singer, heartbroken, is telling his former lover that if she wants to see him again, she'll have to 'invent' him in someone else, or 'invent' what they could have been. It's a powerful expression of longing and the impossibility of recreating what was lost, making it very memorable.
Marco Antonio Solís brings us a song of heartbreak and a bit of playful bitterness in "Invéntame (En Vivo)". It's about a person who was left by their love interest, who doubted their truth. The singer laments, "Por dudar de mi verdad / Te fuiste ayer" [For doubting my truth / You left yesterday]. Now, the ex-lover is apparently doing well, even changing their style and smiling with someone new: "Que a alguien adornas con tu sonreír" [That you adorn someone with your smile].
But here's where it gets interesting! The ex-lover is trying to say they don't want to lose the singer, but it's too late. The singer's response is blunt and a little bit sassy: "Si quieres volverme a ver, invéntame" [If you want to see me again, invent me]. He challenges them to create a new version of him, to make someone else love them the way he did, and even to give someone else a kiss to see if their skin tingles the same way: "A ver si se te eriza igual la piel" [Let's see if your skin tingles the same way]. It's a powerful and dramatic way of saying, "You had your chance, and now it's gone!"