It's not necessarily a question of cooperation.

The problem can be reduced to logical operators: AND vs. OR.

Do you require longest chain AND a litecoin component?
or is it longest chain OR a litecoin component.

The OR solution is clearly bad, as it throws Bitcoin
security out the window, as we just discussed.

However, the AND solution might be too constraining.
If an attacker were to just hit the litecoin network,
it could prevent consensus, causing split chains or
blocks to be unsolved.

Litecoiners: Idea to make Litecoin importance skyrocket in Bitcoin ecosystem
Today at 07:20:47 PM
 #1
Quick rant: I have always viewed Litecoin as a detraction from Bitcoin and have refused to make mass quantities of physical Litecoins as a result.  I have viewed Litecoin as nothing more than a hedge against Bitcoin seeing a 51% attack due to choice of SHA256 as an algorithm.

But:  I believe I have thought of an idea that would make Litecoin far more important and relevant in the Bitcoin/cryptocurrency ecosystem, by being as ready in wait as possible in case Bitcoin really does experience a 51% attack.

In a nutshell, I view a Bitcoin 51% attack as eventually possible, for one reason:  ASIC production efficiency scales far more than linearly with the amount of money an actor is willing to put into it; a bad actor with $1 billion to 51%-attack Bitcoin with its own custom ASICs will be far more than ten times as effective than ten bad actors with $100 million.

Anyway: here is the idea:  Add a mandatory merge-mining feature to Litecoin so that it is always "merge-mining" Bitcoins, just for pretend, in hopes that one day Bitcoin will have the option of "let's subscribe to the Litecoin chain" (as a secondary means of block validation) as a way to resolve a future 51% attack on Bitcoin's SHA256-based chain.

Here is sort of how it would work:

1. Add a new requirement to the Litecoin chain such that a valid Litecoin block must contain either a record of the most recent Bitcoin block header hash, or a repeat of the hash found in the prior Litecoin block (with a limit of repetitions).  Litecoin blocks that contain outdated Bitcoin intelligence should be disfavored by nodes capable of detecting that.  Further impose the requirement that Bitcoin block headers must be represented contiguously in the Litecoin chain - Bitcoin blocks cannot be skipped (which shouldn't be a problem, when Litecoin blocks happen 4x as often as Bitcoin)
2. In the event there is an active Bitcoin block chain fork, the requirement is loosened such that the Bitcoin block header hash requirement can be satisfied by any leg of the chain, not just the one Bitcoin considers valid.
3. Add a feature to Litecoin clients that allow Litecoin users to decide to prefer or not-prefer branches of a Bitcoin fork while one is in progress.  The default for this should always favor the Bitcoin leg with the most longevity, and should disfavor long chains that suddenly appear to replace a large amount of the known Bitcoin block chain.  The user/miner/pool-op should always have an easy way to have the final say, such as by pasting in a preformatted message either exiling or checkpointing Bitcoin blocks.

Anticipated benefits:

1. Bitcoin users would have a ready made remedy to a 51% attack that they can switch to:  Bitcoin users can simply add the requirement that if a Bitcoin block header hash makes it into the Litecoin chain, that its proof of work should be given a bonus.  Litecoin community could create and maintain pulls to the Satoshi client that cause it to subscribe to the Litecoin chain and incorporate it as intelligence toward block validation and resolving block chain forks.
2.  Bitcoin would have an easy way to add an emergency upper bound to block creation, just in case an enormous amount of power suddenly appeared.  By turning on an optional must-appear-in-Litecoin requirement, the Bitcoin community could switch on an upper bound of 1 block per 2.5 minutes if it was deemed necessary.
3. Litecoin would be seen as far more important than a wannabe bitcoin knockoff without added value by those who see it that way.
4. Bitcoin's blockchain would be re-democratized to CPU/GPU users without forcing the Bitcoin community to switch to scrypt, they'd have more decentralized influence on bitcoin than those with the means to buy/make ASICs
5. The legitimacy of Litecoins would increase greatly - people would see the value of Litecoins in their role of protecting Bitcoin, and would potentially vote for the longevity of Litecoin by offering to accept LTC for goods and services, thereby increasing their value.
6. I'd start making Casascius Litecoins if you guys did this and did it well.

I'd call the concept "marriage-mining".  By doing something like this, LTC gives a nod to BTC's importance while adding synergistic value to BTC that LTC can benefit from by association.