Once LTC gets segwit, all LN development will move there because who wants to develop under crippled mode (no segwit) when you have LTC, which is a BTC clone which actually scales and has the network effect of the original alt?
There is only one problem with your scenario - hardly anyone uses Litcoin. In the last 24 hours were only 6,798 litcoin transactions. see
https://bitinfocharts.com/Why on earth would all the LN development move to a coin nobody uses, and hence no fee profit can be made for it
because nobody uses it?
As things stand only ETh is a possible threat to BTc, because people are using it (there were about 87,000 transactions in the last 24 hours on ETH)
though i dont care for LTC or ETH
LTC would gain traction due to the centralists of the DCG
here is a list of those prominent services in DCG portfolio that have alot of sway of the whole crypt-onomy
-blockstream
-btcc(litecoin inventors brother)
-bitpay
-bitpesa
-changtip
-coinbase(litecoin inventor)
-coindesk (puppetmaster of propaganda owned by DCG)
-gyft
-kraken
-purse
-shapeshift
-xapo
plus many more
imagine if all of them (shh they are already becoming) start being LTC friendly. ETH wont stand a chance with being 'merchants accept' available