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As a Latam Platinum member, you have got access to all those lounge which admit OneWorld (OW) Sapphire members when flying on one of the alliance's airlines.

As far as LATAM's own lounges are concerned, this should definitely grant you access to those in SCL, EZE, GRU, BOG and MIA. However, I am not sure, what the policy is at their other hub-like stations such as LIM, GYE and GIG, where lounges are operated by a third party.