I don't want to join my colleagues for lunch, but I am an intern so joining is important for relationship building.
I don't know how they manage to have lunch everyday together but they do. Am I forced to join them in this situation?
Am I forced to join them in this situation?
Absolutely not. You are not forced to eat lunch with them every day.
Yes, it is true that having lunch together strengthens the professional relationship, but you should do it when you feel like it (and when your budget allows for such).
Next time they invite you, and you are unable or don't want to go, politely thank them for the invitation and decline. No need to give lengthy explanations, or make up excuses.
Why can you not join them? Is it a money or time issue?
If it is a money issue, then they will understand. They do not expect that an intern is paid at the same rate as they are, and cannot spend at the same rate. In this case make a budget and go out with them on set days. An example might be every Friday and every other Wednesday. You should be upfront about why you are doing this. There is nothing embarrassing about being financial responsible. On those days you do eat in the office join anyone that does the same and expand your horizons some.
If it is a time issue, then the same sort of thing applies. "Sorry guys, I can't make it today due to work on project X".
You can still build on the relationships on the times you actually do go to lunch.