Doge wants LTC to participate in this, but what if LTC refuses? It would make doge look bad.
From my understanding it's not up for LTC to decide anything. LTC doesn't have to do anything. It's just that miners that are mining the scrypt coin with the highest hashrate will be able to also mine dogecoins simultaneously. Currently the scrypt coin with the highest hashrate is LTC, but that can change at any time in the future. From the reddit thread:
What this does not mean is that we're tying us to Litecoin. What we do is accepting Proof of Work from their miners if they happen to hit our difficulty target.