So, how a network gets larger?
Well that is a good question. Merchants accepting LTC along side BTC is good but has a small network effect. Merchants that only accept LTC provides more a network effect. Even more useful would be developing the supporting infrastructure? Where is the LTC equivalent of bitpay to provide turnkey solutions for merchants? Where is a US/EU based exchange which provides LTC/USD pairs? If LTC is less liquid and harder to adopt then outside the dreams of those holding large coins it is improbable to think merchants will adopt it. I mean lets look at Bitcoin. Bitpay makes it very easy and risk free to accept. Companies can price in USD, get paid in USD, receive a guaranteed amount of USD, and have funds in their bank account as fast as credit cards. Combine that with no fraud and low fees. Even with that Bitcoin adoption has been slow. Now compare the current LTC situation? Honestly think its network is going to grow faster?
The problem is that as valuable as a well run "LTC Bitpay" would be it would only be "as good" as Bitcoin. LTC wasn't ambitious enough and ended up a shallow copy of Bitcoin. That makes it very hard to outgrow its big brother. It may simply be impossible. A crypto-currency which is designed from the ground up to be superior to Bitcoin in areas where Bitcoin is inefficient likely has more of a chance of carve out a niche. Bitcoin is ill-suited for small transactions. A radically different crypto-currency designed to use a floating ledger would provide less security but would provide a superior platform for quicker, lower cost small transactions. Is it enough to compete with off-chain txs? I don't know but at least it would have a competitive advantage. Still nobody would likely be storing huge sums in this complimentary currency due to potentially lower security but it could be successful alongside Bitcoin.
Honestly (and no doubt some will disagree) I see only two highly successful alt-coins in the future
a) one which tries to compliment Bitcoin (and please no "silver for Bitcoin's gold nonsense)
b) one which is so vastly superior to Bitcoin that it displaces it as the dominant currency
No alt-coin to date has been ambitious enough to attempt either.