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Is your LN wallet a custodial wallet (e.g., Blue Wallet)?
With Wallet of Satoshi and CoinOS, you can deposit on-chain, and then access (i.e., spend) those funds via LN.
Otherwise, how do I fund a LN ‘wallet’?
You can use an exchange that has support for LN. You can either buy bitcoin and withdraw LN, or some (e.g., Bitfinex) will let you deposit on-chain and withdraw via LN. Some (e.g., Paxful) charge a fee for withdrawing via LN.
Exchanges with support for Lightning Network https://cointastical.github.io/Exchanges-With-LN