I'm guessing at a couple of things here but given climb to FL110 rather sugests that Heathrow were on easterlies. In which case your flight would cross the track of Heathrow inbounds leaving LAM on a heading, usually 265, for positioning downwind left hand. The inbound would leave LAM descending to FL70 or 80 depending upon the QNH. If you were suddenenly given stop at 6000 ft it suggests that the TMA dep controller had made an initial bad error of judgement and was now trying to correct the matter. He probably thought you could out climb the inbound before your tracks came close. Given that your climb rate was 4000 ft/min it looks like a very bad initial judgement but a very good decision to stop you off before safety was compromised. Did you get anything on TCAS?
Now for the sobering up bit. Late last year there was an airprox caused by a climb to a FL followed by a stop off at an altitude. On this occasion there was a big difference between 1013 and the QNH. The pilot stopped of at FL60 when the controller was hoping for 6000ft and then there was a loss of separation. I guess technically the controller should give the QNH but in the heat of the moment it was forgotten. And the pilot didn't pick up on it.