Second layer solutions were created because of the inefficiencies of the main chain, primarily in terms of price and confirmation time per transaction. The idea was to have a majority of transactions happen off-chain to save on the size of the entire block chain. This was argued to improve security as more full nodes could come online to secure the network from nefarious miners.
The bitcoin maximalist block size argument goes as follows:
The first layer must be made up of small blocks which causes transactions to become slow and expensive.
Having a small blockchain increases the security. This is usually portrayed as a zero-sum trade-off that is built into the physics of blockchain technology. IE: you can either have high security or price/speed efficiency(big blocks).
This argument has already been debunked when considering current technology and the rate of technological progress. But let's see how this zero-sum trade-off holds true in regards to using the lightning network:
Assuming the fees on BTC were eventually to grow to be $1000 or more per transaction, which they will if BTC is to see mass adoption in spite of the fees gradually increasing.
Bob has $50,000 dollars in his BTC wallet and he would like to move some into his lightning wallet so he can utilize BTC for day to day transactions. He would have to pay $1000 to move any amount of his cold storage into his lightning wallet. How much would he have to move to justify spending such a large transaction fee? Well, he wants to maximize the amount in his cold storage, because it is the safest place for his life savings. Let's say he wants to move a quarter of his life savings from cold storage into his lightning wallet. He would pay $1000 to move $12,500, so he would effectively be paying an 8% movement fee. That seems a little high, so he has to debate whether or not he wants to pay such a high premium to ensure that 75% of his life savings is kept in cold storage. At least this way 75% of his life savings is very secure and he knows that it will be safe. But Bob decides that an 8% fee is too high so he would like to move more of his cold storage, to make the fee more worth his while. If he moved half of his cold storage he would effectively be paying a 4% transaction fee to move $25,000 into a much less secure network. He is paying 4% to move half of his net worth to a wallet which is much less secure than his cold storage. Though the percentage is much more bearable, he still now has half of his life savings off-chain, outside of his cold wallet, in a much more vulnerable position.
So it becomes a zero-sum trade-off between security and fees, in the same manner that the BTC maximalist describes the zero-sum trade-off between security and big blocks.
Now we will look at another example of how the second layer relies on the first: Alice is new to BTC and she agrees to get paid in BTC for the work that she does. Since the fees are $1000 per transaction she can only get paid via the lightning network. She only makes $10,000 per year so if she wants to pay a low 4% transaction fee she would have to work for 2.5 years and not spend any of her money. This is impractical because she has expenses, but for the sake of arguments let's assume that she can accomplish this. In this situation she has to keep her life savings in an insecure lightning wallet for 2.5 years. She does not get the benefit of utilizing the security of the BTC blockchain, she is too poor to do so.
Regardless of how efficient off-chain technology is, it will always be limited by the inefficiency of the main chain. There is no way to get around this since the main chain is the on-ramp and off-ramp toward second layer solutions.