lol I think the question should be " do cats like yorkies" lol, if your cat does not like your two older pups he more then likely will not like a pouncing puppy lol. Lulu will want to play with the cat, he will chase after it as it will be almost the size of him lol.
Walks to the ocean sounds fantastic, I had two females that LOVED to swim, LOVED the water, summers they were like sea otters always in their large kiddie pool. I just introduced Cody to the kiddie pool, he's not to crazy for it lol. You will have to see how Lulu likes it, if you start them young going in the water most will enjoy cool dips on hot days. Sand
. If you let any of your dogs take a dip or swim in the ocean water make sure you give them a good bath when you get home, the salt from ocean water will dry out their skin.