Increased hash rate == increased network security.
Also, litecoin is certainly not at all immune to ASIC.
Litecoin is not immune to ASICs but ASICs won't give a hashrate boost on mining Litecoins as much as it does for Bitcoins. You are right, as Litecoin price goes up, ASIC litecoin miners will inevitably come out when it becomes profitable.
I don't agree that "Increased hash rate == increased network security". When ASIC bitcoin mining is widely available, if you have the same number of people mining, the network won't be more secure just because the hashrate is higher. It's all about how much $ it takes for an attacker to come up with enough hashrate to 51% the network. ASICs might eventually increase the network hashrate 50x but that does not mean the network is 50x more secure if it costs the same amount of money for someone to successfully attack the network.
Take for example, if someone found a way to optimize the miner software to be 10x better hashrate and it works on CPUs, GPUs, FPGAs, and ASICs. Then all of the sudden, the next day EVERYONE uses the new miner software and the network hashrate jumps from 50 thahs/s to 500 thash/s. Is the network now ten times more secure?