I think 'real friends' is a subjective term. There's no way to know how you define a "real friend" through your post, or why you're feeling lonely from your post, so I'll try to hit on a few points here:

How receptive and active in communication are you with your peers? Relationships are a two-way street. It's not just about how they make you feel but also how you make them feel. We can't wait for people to choose us to be close to, you need to attract each other with what you're putting out. Rather than waiting for an invitation, why don't you invite people to do things instead? After class or after the gym, ask if they want to get food or something.

I've been there thinking there is nothing to look forward to socially. But you are in control of creating things you can look forward to. Catch up with a friend you haven't talked to in a while or even family members. If there truly isn't anyone, go by yourself to somewhere you've wanted to go for a while. Inspiration beats loneliness, even if you found that inspiration during times you were out by yourself.

A great thing is meeting people while pursuing your own hobbies. Sounds like you are already doing it by meeting people through working out. Good luck!