LHR T1 Lounge?
 

We are flying Club Europe on BA from DUB to LHR arriving at T1 about 7:30 am. We are meeting our children flying UA to LHR arriving at T1, 4 hours later. One of us also is AA Platinum (Oneworld Sapphire). Can we use the BA lounge at T1? Also, can we meet our children at the gate? Thank you for your helps.

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I'm afraid there is no arrivals lounge you can use at T1, nor will you be able to use the departure lounge as arriving passengers.

And unfortunately neither can you stay airside and meet your children at the gate because DUB is treated as a domestic arrival so you are in a separate zone of the terminal.

All you can do is meet them at T1 international arrivals.

If you have four hours to kill, you could take the free train to T5 and go to Carluccio's, which does a decent breakfast.