So this statement is "you can scale blockchain tech by using another tech in its place that doesn't offer the same guarantees".
There's the possibility of double spending by committing to the bitcoin blockchain an old version of your "database", but then you would face the penalty of having your entire balance confiscated by the other party.
More details here: https://bitcoin.stackexchange.com/questions/67141/how-is-a-d...
Only if the other party notices in time that you did this. You are reliant on active monitoring of the blockchain to know that your transactions actually happened. And the more you want to scale (i.e. the more transactions you do on a single Lightning channel without settling it on the BTC blockchain), the bigger the risk becomes.
I would argue that Lightning's biggest security issue is having to store your private keys on an Internet connected device. I don't know if further improvements can be made in this area, for example allowing for some kind of 2FA, like multi-sig on the base layer.
There are conditions on every payment system. With bitcoin you also have something to do to prevent double spending: wait for some number of confirmations (and making sure you're on the right chain).
And "double-spend protection guarantees of blockchains" is very dependent on the cost of doing a 51% attack, so it's not strong by itself. It's very strong in bitcoin only because the quantity of hashrate/money required to do one is astronomical. It's not so strong on small blockchains.
And I fail to see how the risk increases with more transactions on a single lightning channel.
The risk doesn't increase with the number of transactions on a channel, that was a wrong statement from my side. What I was thinking of is that the risk increases the more your transact through Lightning instead of regular BTC. Basically, the more of your BTC is caught up in Lightning channels, the higher the value of attacking you with a double spend attempt.