We will be in Rome on July 7 and 8, 2019. July 7th is a Sunday and Vatican Museum is close. So we have to reserve Monday July 8th for Vatican city. Sunday July 7th will be dedicated to ancient Rome including Colosseum, .... However, July 7th is the first Sunday of July and most of the major attractions are free and hence very crowded. Online reservation is not possible for this free day. I wonder if there are any alternatives to skip the lines. Does Roma Pass work in the free day? Any other suggestions? Thank you.
You can't skip the security lines and there are no ticket lines during the free Sundays.
Your best bet is a small group tour, like with Walks of Italy.
A small group tour of Rome's ancient exteriors might be a very good idea for the 7th! They just can't cover the interior of the Colosseum on free Sundays, or the Forum and Palatine either, as far as I'm aware.
- I wonder if there are any alternatives to skip the lines.*
Yes, wait until Monday.
I would just forget about the biggest attractions, except maybe a walk through the Forum or other large outdoor venues. I think I would do some planning to hit lesser known venues that maybe won't attract the crowds, but have interest to you and maybe would have been further down the list and skipped due to added cost.