If you see a smaller wild cat it’s most likely a bobcat, not a lynx. We have very few if any lynx left in Michigan. Although it wouldn’t surprise if some roam through from time to time.
Both are fascinating animals. And, true to all cats, they are only seen when they want to be seen. Which means that you may never see one in your entire life. In fact, I’ve only seen a handful of bobcat. A couple while driving, couple in the woods and that’s about it. More often I see their sign, which reaffirms that they do exist.
A really large bobcat might be 40 pounds. Most are in the 20’s. Even still, it’s amazing what they can take down - including full grown deer. I’ve seen the after affects of fresh kills in the snow.
I’ve never heard of an unpleasant encounter with a human though. If you see one consider yourself lucky and take a picture if you’re quick enough!