On a sidechain/spiderchain, when the "Orchestrators" try to steal coins, this is very similar to a LN member trying to close a channel in an old state. Nothing is changed regarding the token supply, but there is an unintended ownership change which would not be possible only using on-chain methods.
The only difference I see is that a sidechain in theory could be buggy in the sense that some unintended function leads to a supply inflation of the pegged token (let's say something like the Bitcoin overflow bug in 2010). From my limited understanding that would not be possible in LN, not even taking into account milisats, but all sidechains have this theoretical problem. As long as they work as expected though that's not a problem. Where a difference could be possible is if the sidechain stakers cooperate to create such a bug intentionally. This would however damage all Orchestrators, because they couldn't exit 1:1 anymore. So the attacking subset would have to profit purely by operations on the sidechain (e.g. fast sells of the sidechain tokens on exchanges, or buying goods/services) and I cannot imagine that kind of attack to be easy to be profitable as long as the sidechain isn't extremely popular (and of course, it would be detected in one block as a maximum).
This little drawback however is compensated by the big advantage that you can "onboard" people completely independently of mainchain transactions.