Someone has sent BTC on the Bitcoin Lightning Network from their Electrum Bitcoin Wallet to my personal wallet address.
You keep asking basically the same questions over and over again, though other users told you already that you're very likely a victim of some scammer scumbags.
Do you have Lightning channels open in your Electrum?
In your other topics the amount of coins of that dubious transaction is almost certainly too big to be sent successfully via Lightning, especially as you'd need open channels with enough receiving capacity. Highly unlikely that this is the case for you.
When a Lightning channel is opened you lock money in that channel that can be moved around between you and your channel partner. If you and/or your channel partner have more channels open, then routing is possible. Still the amount that can be moved is limited to little less than the channel capacity.
Lightning transactions stay within Lightning normally, so how should this work that someone sends you via Lightning Network some magic amount of coins to one of your wallet receive addresses?
The status of the transaction is pending and has been stuck in the Lightning Network for 3 months now.
That's what the other party wants you to believe. Anyway, it sounds like total bullshit to me. You still think there's any truth in the story of the scammers or that "someone"?
How can I find out why it is stuck and expedite the transaction?
You can't because it's likely fake. Otherwise, provide transaction IDs or other verifyable data.
