So even if LTC is not profitable, people still mine it because they don't need an extra machine to do so. They do merge mining, and all the LTC reward comes as a bonus with Dogecoin mining.
This is the thing, it's not that simple..
For example, if LTC were to go to zero, it would also affect DOGE hashrate, it would go down by the % the LTC reward is in.
Let's assume DOGE gets killed, LTC will just survive with how much hashrate they can get with their reward.
Both of them are profitable, it's much like real mining, mining just the iron can be only slightly profitable, but the by-products like cobalt can be the difference between keeping the mine alive or not.
The thing overcomplicated itself over long run since LTC is a fixed supply while Doge is not...