It means “immediately, right away, on the spot”
Menm kote a
Are all used about the same way.
Lamenm, li bliye tout bagay.
She/he forgot everything immediately
Lè’l pran kiyè enpi l reyalize li te cho anpil, lamenm li jete l atè.
When she grabbed the spoon and she realized it was very hot she dropped it immediately
Fanm nante touche rad Jezi, e li te geri lamenm.
The woman touched Jesus' robe and she was healed on the spot.