Coursing won't make dogs aggressive to other dogs. I have two borzois that hunt and have killed game, including coyotes, and they still adore other dogs. Dogs are smart enough to recognize their own kind.
She may be fear aggressive, especially if she wasn't socialized with other dogs as a puppy or was attacked at some point.
If she's fear aggressing, I would not use a muzzle on her. In her mind, her mouth is her only defense against the scary other dog. Take that away and she'll become far more anxious and reactive. Just make sure you keep her leashed and keep strange off lead dogs from approaching. You might need a spray bottle, a walking stick, or just yell at them if they start to come over and get in her face.
What is your lurcher mixed with? It's common for terriers to be dog aggressive so that may just be the way she is. Even the most dog aggressive dogs can learn to ignore other dogs on walks though, and you'd only have a problem if the other dog got up in her face.
The simple way to work on it is this:
Right now she thinks other dogs = Scary Bad. So she tries to make them go away by acting mean and scary before they have a chance to.
The way to change this is change the way she thinks of other dogs. This means keeping her below threshold. The threshold is the point where she starts reacting to whatever is stressing her out.
Find a treat she will drop everything for. Something super special, that she ONLY gets when other dogs are in sight. Since she's a sighthound something smelly and goopy is a good bet. We use teriyaki duck skin for serious conditioning. Another cheap alternative is hotdogs sliced into medallions the thickness of a penny, wrapped in a paper towel, and microwaved until they are like beef jerky. Then I throw them in a plastic bag with a TEENY bit of garlic powder and shake it up. The dogs can't resist.
How close can she get before acting aggressive? 10 feet? 20 feet? 100 feet?
Find out what that distance is for her, and don't push her over it. Take her within view of another dog at a distance she is comfortable at. While she is standing at ease, give her one of the special treats.
Do a little bit of training with her while the other dog is at a distance. Especially if she's starting to fixate on it. Walk away, have her look at you. Give her wonderful treats for looking at you. Don't be stingy with the treats. Try walking a tiny bit closer to the dog than before and load her up with treats again.
The idea is to slowly work closer and closer to other dogs until you are able to walk past them without her fussing. You'll want to try and prevent her from being over threshold if at all possible while you're reconditioning her. This may mean walking her later at night when there are fewer dogs out. Or turning around if you see one approaching, or crossing the street to avoid them.
Don't correct her. Sight hounds are sensitive and if you punish her for reacting to a dog she will only see it as, "Whenever I see another dog my human hurts me!" And that will make her aggression worse in the long run.
If you're interested in a book, Click to Calm works on the principles I listed and is very effective for teaching reactive dogs to calm down and stop reacting. The nice thing about it is you don't need a clicker to use the principles in the book.
Edit: With small animals you just need to be very careful. If you let her out in the yard she may just catch some rabbits and squirrels, that's the way these hounds are. You can teach them to ignore small animals on walks and in your home, though I'd never leave them unsupervised together if, say, you have a pet rabbit. Both my borzois learned to leave my chickens, flying squirrel, and chinchillas alone. One of the dogs is very trustworthy and totally ignores them. I suspect he'd even ignore them unsupervised. The puppy wants to eat them very badly, but doesn't because she knows they are not hers. Most hounds are able to learn that running is situational and control themselves when they aren't in the field.
