Visited the Lima Salones a couple of days ago. Apparently you need a "pass" or "coupon" which says Taca invites you (in Spanish it's Taca Invitamoste or something like that). It's approx a 3x5 card which is good for salones entry.

I of course didn't have one. I talked with the front desk lady for about 10 minutes in spanish and then confirmed a bunch of it in english just to be sure. Then I found a Taca rep across the hall at a gate. He brought us back and we were in.

1) Find a Taca Agent and explain that you are on a Distancia Biz Ticket and want to use the lounge
2) Since you'll be connecting you could remind them that the airport you checked in at doesn't have the invitation coupons to the lounge (EZE doesn't for example)
3) They'll escort you to the lounge.

Only a small portion of the Taca staff in Lima actually speaks english more than a few words so be warned bring your dictionary and practice up.