```python
"""Drain labelled items across planned lanes, round by round."""


def drain_lanes(plan: list, items: list) -> dict:
    if not plan or not items:
        return {"order": [], "rounds": 0}

    queues = {lane: [] for lane, _quota in plan}
    for label, lane in items:
        if label in queues:
            queues[lane].append(label)
        else:
            return {"error": "Unknown lane: " + label}

    order = []
    rounds = 0
    while True:
        rounds += 1
        for lane, quota in plan:
            queue = queues[lane]
            taken = 0
            while taken < quota and queue:
                order.append(queue.pop(0))
                taken += 1
            if taken < quota:
                return {"order": order, "rounds": rounds}
```