Lightning can take some of the load now, but not that much (there's about 100 BTC on the LN as of today, October 28th). There's probably a small amount of people using lightning for which a big spike in on-chain transactions would be unnoticeable; they've already got as much money as they need into channels already, enough to ride out the spike until it dies off. In the end, Lightning will help to relieve the impact of on-chain transactions queues far more effectively, but not yet.
LN is the worst place to be , if bitcoin suffers a massive spam attack,
as their is a vulnerability if the ONCHAIN does not have enough transaction capacity.
https://bitcoinmagazine.com/articles/here-s-how-bitcoin-s-lightning-network-could-fail-1467736127/The Lightning Network’s Failure Mode
The Lightning Network failure scenario described by Todd, takes place when a large number of people on the Bitcoin network need to settle their Lightning Network disputes on the blockchain in a relatively short period of time.
“We do have a failure mode which is: Imagine a whole bunch of these [settlements] have to happen at once,” Todd explained. “There’s only so much data that can go through the bitcoin network and if we had a large number of Lightning channels get closed out very rapidly, how are we going to get them all confirmed? At some point, you run out of capacity.”
In a scenario where a large number of people need to settle their Lightning contracts on the blockchain, the price for doing so could increase substantially as the available space in bitcoin blocks becomes sparse. “At some point some people start losing out because the cost is just higher than what they can afford,” Todd said. “If you have a very large percentage of the network using Lightning, potentially this cost is very high. Potentially, we could get this mass outbreak of failure.”
The way the Lightning Network works, a user must be able to issue a breach remedy transaction in order to keep their counterparty honest.
If a user is unable to make the proper transaction on the blockchain in a certain amount of time, their counterparty may be able to take control of bitcoins tied up in the smart contract between the two parties.
LN is no solution to bitcoin's onchain limits, if those onchain limits are pushed to the max,
in fact it would make matters worse if LN users starting closing channels as the onchain fees increase.
Segwit only gave a ~1.7 megabyte size increase from the 1 megabyte.
Using LN is only safe, if bitcoin onchain limits are not being exceeded.Which is why using litecoin with LN is safer than using bitcoin with LN, as litecoin has onchain transaction capacity to spare.
*Onchain Capacity Matters*