I think your goal weight of 175 sounds perfect for now.
I'm four inches shorter than you are and my first goal was 160, so yours and mine are pretty comparable.
When you get to 175, then you can assess factors like how you feel, the size you're wearing, your body fat percentage, health indicators like blood pressure, and most importantly, how sustainable that weight feels to you. You might decide to maintain there for a while or you might set a new goal, but for now, 175 sounds ideal.
The body fat ranges aren't in any way related to BMI. They're two totally different animals. BMI is strictly a height-weight correlation and is the same for everyone. Body fat percent measures your body composition and is unique to you. My personal belief is that body composition is a
far better indicator of health and fitness than is BMI.
More muscle is always better! Your LBM of 125 pounds is on the high side for a woman, probably because you've done so much weight bearing exercise just in the course of everyday living! True, you also have the skin, blood, water etc necessary to sustain 225 pounds, but you also have more muscle than most normal-weight women. It is very much to your advantage because muscle is the calorie burner in our bodies. The more muscle you have, the more calories you can eat to maintain your weight (or to lose). And you will look so much better when you get to your goal than someone with less muscle.
The reason I said that it would be fairly optimistic to assume your LBM stays consistently at 125 for the entirety of your weight loss is that usually some LBM is lost along with fat. We just try to minimize the LBM loss and maximize the fat loss by supporting our LBM and muscle mass with good nutrition (lots of protein) and weight training. You may end up with an LBM around 115 - 120 pounds, but it's very hard to say at this point. So let's not even speculate about it!
The one thing that I can tell you about your goal weight is that you'll probably know when you're reach there. You'll be feeling fit and athletic, you'll be thrilled with clothes shopping, your doctor will think that you're awesome, and most importantly, you'll be living a lifestyle that you're certain that you can comfortably sustain for the rest of your life. You'll feel comfortable in your skin and you'll feel like you've stripped away all the layers and this is the "real you". You'll just feel that a particular weight is right for you. I know from all of your posts that you're sensible and thoughtful and you won't go chasing after low scale numbers just for the sake of reaching a number. Trust your instincts.
Reading your recent posts just gives me such a thrill -- it seems like you've just caught on fire lately! Not with weight loss, necessarily, but with your whole attitude. There's no doubt in my mind that you're going all the way!!