Hi explorer98 -
Yours is a question that's too broad to answer without additional information. A good guidebook and local websites are also your first and best resources for browsing attractions, tours and whatnot. A couple websites to spend some time with:
Personally, I don't think tours are at all necessary in the Cinque Terre (I do hope you are staying there and not doing it as a day trip?) as there isn't much more to do than explore the small-to-tiny villages on foot, take a ferry ride (in season) and/or hike. Take a swim, maybe, if warm enough to do so. Folks with longer stays sometimes choose to explore a bit further afield to Porto Venere, Santa Margherita Ligure, etc. Hiking the regional park (the villages fall into this area) is one of the biggest, if not the biggest, draw for many though. Website:
If not hiking, your options for getting from village-to-village will be trains and/or ferries (excluding Corniglia, which the ferries don't service.)
I'm pretty sure tours aren't necessary in Lucca either but I'll defer to others on that one. Walks and bike rides along the city walls is a very popular activity.
But in the end, how to spend your time depends on your personal interests, your ages and physical abilities (the CT isn't a great place for folks with mobility challenges,) ages/abilities of any persons traveling with you, how many nights you have to work with, and time of year/tolerances for crowds (May promises to be VERY busy in the CT.) I would avoid the May 1 holiday weekend - May 1 falls on Friday this year- for SURE. Also, accommodations book up fast and early for high season so you're already somewhat behind making reservations for May.
Editing to add: regarding tours, I'd strongly advise against any sort of group tours of the C.T villages due to the heavy crowds. You stand a much better chance of escaping the peak-hour masses if you can escape to the upper reaches where most of them do not venture.
Anyway, the more you can tell us about yourselves the better we can assist. :O)
But do get a good guidebook + spend a little time with the websites for initial ideas?