Main chain BTC can handle something about 300k tx per day without increasing fees, open and closing channels need to be done using standard tx on main chain. So the question is if we will have large world adoption, can LN can produce 300k tx per day (sum of opening and closing txs)?
The answer is yes, but not anytime soon. Also, it's a function of how frequently channels are opened and closed, which can be estimated, but is not "really" predictable.
If you read the LN whitepaper [link], it mentions in the conclusion that "to enable 7 billion people to make two channels per year with unlimited transactions inside the channel, it would require 133 MB blocks"
As Wikipedia notes, "the Lightning Network ... has been touted as a solution to the bitcoin scalability problem".
So part of the objective of the Lightning network is to reduce load on the Bitcoin blockchain in order to allow a higher rate of Bitcoin transactions than would otherwise be possible.
Without LN, or some major changes with similar effect, Bitcoin would likely lose market share to other crypto-currencies with better scalability and faster, cheaper confirmation of transactions.