But what if tx1 doesn't make it into the block on time?
Unlike tx2, tx1 confirmation time isn't critical, if takes longer than we expected, it's just an inconvenience for us at worst. And to make sure it won't take too long we only need to include competitive fee proportional to modified tx size.
If there is enough space in the block, tx2 will still count as using that extra space it's parent bought, I suppose?
I think so, I'm not sure however, maybe it can be implemented different ways. But even if it counts as using the extra space, that doesn't upset us much. Because what's really important in this case is confirmation time. We only loose fee for that extra space.
Besides if, all transactions in a channel are sent off-chain and only the opening and closing ones are sent on-chain, wouldn't that mean that first we would need to send tx1 to prebuy space, and then tx2 to maybe use that space?
I'm not sure if understand you here. In level 3 LN (one which needs segwit) it's important that all commitment txes prebuy enough space for certain outputs, so that txes spending those outputs are readily confirmed. If one of channel participants refuses to use space prebuying, it's a red light, another channel participant should immediately close the channel, or abstain from channel opening if it's not opened yet. The opening tx should also prebuy space enough for a commitment tx.
We are also still left with an arbitrary 10 MB limit, which may be enough only for a limited amount of time.
I think numbers here are completely arbitrary. They can be adjusted according to community consensus on optimal blocksize. Moreover, they can be adjusted by a slow dynamic blocksize algo, if one will ever be adopted.