On the second floor, I have the main bathroom. On the other side of this bathroom wall there is a big closet. I would like to turn the closet into a bathroom.
Is it as simple as sharing the sewer lines and water lines from the main bathroom?

Is it as simple as sharing the sewer lines and water lines from the main bathroom?
Not quite but almost! Here's how it should go down. Most bathroom groups are roughed in like this.
Toilet connects to the stack vent. You may have to cut a wye into the old toilet drain to pick up the new group. The Lavatory connects to toilet drain and runs a vent off the top the stubout tee to revent back into the existing lavatory vent .The toilet wet vents through the lavatory vent and the tub/shower connects to the lavatory drain and is wet vented by it. This is a normal rough in and is acceptable both by local and state codes and also The Standard Plumbing Code Book in 90 percent of the country. Check your local codes to make sure you're not in the excluded 10 percent..
Another that you might consider is connecting each new fixture to the old fixtures drain line and using the lavatory vent for both groups. This would worki in my area. You have 12 fixture units total between the two groups. A 2" vent will handle 20 fixture units so you'll be OK there. Check local codes to see what's best for you. I would suggest taking the new bathroom water supply off of 3/4" mains instead of taping into the old bathrooms 1/2" branch. Good luck, Tom

Not quite but almost! Here's how it should go down. Most bathroom groups are roughed in like this. Tom

Tom, thank you very much for taking the time to answer my question. I think I've read your response about 20 times and its finally sinking in.
I have no idea what's behind the wall and how things are connected. The house is 76 years old, and Lord knows what codes they had back then and how it is all connected.
I'll probably write back with pictures of what I have and ask for more advise.
Shant

Good morning Shant,
Pictures and a diagram of what you have would be helpful in laying out your remodel job. Inn order to help I'll jnheed all the details you can feed me. Material the drainage pipes are made of. The lay out of the old bathroom, Future problems that you can see etc. Installing a full bathroom group is major surgery, a permit will have to be pulled and code followed. We can help but do you have the necessary skills and tools to do the job? What area do you live in and what Plumbing Code do you fall under? Talk to me! Regards, Tom