for a 0.027BTC transaction the fee I paid was 0.000164BTC which is comparable to the on-chain fee.
I'd expect to use LN for small transactions. This is worth more than $1000, and I would keep such amounts on-chain.
This was on Electrum trampoline.
I've used several LN wallets in the past, but never this one. Does it at least show you the fee before sending the payment? You paid 0.6% fee, which is a lot. From what I've seen, most LN node owners "complain" that they don't make any profit. It sounds like the only route for your (high) payment was through a node with much higher fees than average.