This is something I was going to post about a little while ago but I stopped meeting the dog in question on walks but bumped into him again today!
I walk my Golden Retriever (9 months) on a lead and a few times now we've met a BIG dog. On chatting to the owner, she says her vet thinks the dog is a Great Dane/Rottweiler cross. Her dog is always off lead. My dog is on lead because he has no recall and is too friendly (he wants to be best friends with every person and dog he sees!)
Anyway the "problem" (if it is one, I'm hoping it isn't) is the way her dog approaches mine. Today for example, he sees my dog and immediately puts his head down and starts approaching staring all the time. Then he lay down, but was still staring. I was walking past parallel at the time. He then got up and approached again, quickly but not quite running. When he got to my dog he barked and growled a little. My dog was a little nervous and moved away which resulted in big dog "chasing" my dog a bit in circles (as my boy was on lead). The lady's husband called the dog but it took a little while for the dog to respond. When I looked up I spotted the lady looking quite worried, which worried me a little. What did she think would happen? Does her dogs behavior worry her?
Helga, I would be a bit worried by this behaviour because it shows the other dog is fixated on your goldie. It's common in herding dogs, that stare and the stalking and laying down like that, and put to good use when they are herding sheep, but it's not a good thing otherwise. My guess is that the other dog is (at least sometimes) reactive. One of the things I've done to try and train Dog2 out of being reactive is learning to break that stare. If left to do it then there may be growling or a bit of aggression at the meeting, as you found out.
If you see a dog doing that, it's best to avoid it if you can. The other owner should have been more alert and called her dog back sooner, especially since your dog was on a lead.
Thanks redwing I knew the lying down looked familiar but couldn't place it but it was in my uncles sheepdogs! It was the staring that unnerved me a bit. The owner did call the dog but he didn't respond at first. We were on the beach but the tide was coming in so I was as far away as I could get.