I dont believe Lacsa/Grupo Taca has a dedicated English nonrev line. Acording to our pass travel Listing is not required for travel on Lacsa.
I have called Grupo Taca for travel btw EZE and LIM (flights operated by Taca Peru) and they were extremely helpful- they even gave me actual numbres for seats available. Spanish is my first language so all interactions were in Spanish, not sure if you will have the same luck if you communicate in English.

Regards,

Chepos