Database

db={"coll1":[{"_id":"some_unique_id1","plan":{"type":"premium"}},{"_id":"some_unique_id2","plan":{"type":"free"}}],"coll2":[{"_id":"some_unique_id3","user_id":"some_unique_id1","eligible":false}]}

Query

db.coll1.aggregate([{$match:{"plan.type":"premium"}},{"$lookup":{"from":"coll2","localField":"_id","foreignField":"user_id","as":"coll2Lookup"}},{"$unwind":"$coll2Lookup"},{$addFields:{"coll2Lookup.eligible":true}},{"$replaceRoot":{"newRoot":"$coll2Lookup"}},{$merge:{into:"coll2",on:["_id"],whenMatched:"merge"}}])

Result