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


def drain_lanes(plan: list, items: list) -> dict:
    if not plan or not items:
        raise ValueError("Plan and items must be non-empty.")
    
    queues = {}
    for lane, _quota in plan:
        if not isinstance(lane, str) or not lane:
            raise ValueError("Lane must be a non-empty string.")
        if not isinstance(_quota, int) or _quota <= 0:
            raise ValueError("Quota must be a positive integer.")
        if lane in queues:
            raise ValueError("Lane declared twice.")
        queues[lane] = []
    
    for label, lane in items:
        if not isinstance(label, str) or not label:
            raise ValueError("Item label must be a non-empty string.")
        if not isinstance(lane, str) or not lane:
            raise ValueError("Item lane must be a non-empty string.")
        if lane in queues:
            queues[lane].append(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}
```