AFAIK it's 2,5 minutes. But that isn't important.
You're obviously right that there presently is no real need for LTC to get more capacity. But the opportunity Litecoin has is just the "media buzz" it would get if it preceded BTC with a working Lightning Network. It would be able to market itself as the "cryptocurrency ready for billions of users".
I'm however not really convinced it would reach BTC's market cap (at least not fast, and the higher orphan rate could be a factor that would favor BTC) but it could reach the market cap of Ethereum without problems and get some use by merchants - and in this case for OpenBazaar a LTC addition would already be a "win".
But I think if BTC gets Segwit, LN and other second layer solutions before - let's say - mid-2018, then it's almost sure it would continue to be the undisputed leader of the "cryptosphere". Only in the case of a hard fork or an eternal "scaling debate stalemate" (let's see if UASF can break it) I see that leadership in danger.
yes it is 2.5 minutes block time for Litecoin: http://www.coindesk.com/information/comparing-litecoin-bitcoin/
LTC here is more of a testing grounds,I agree,it doesn't really need the bigger blocks at the moment
but it might in the future,also it is good for Segwit popularisation -if it works on Litecoin
this could lead to a swing in the pools percentage signalling for Segwit