I'd say it depends on what other areas in Tuscany you'll be visiting during your trip. You have basically two choices:
either take the
A1 that passes through Florence which takes a little more than 3 hours OR follow the
E80/Via Aurelia that goes through Grosseto up along the coast. This one adds about an hour to the drive... smaller roads not just a more round-about way to get to Lucca.
Both pass through beautiful areas that merit seeing - the A1 passes near
Montepulciano and
Arezzo. It passes through
Florence. Will you be heading back through here later on? There are many villages near the road but you have to know the exits - you'll have to get off and drive a little in either direction to get to interesting spots, especially for lunch. The only choice on the road itself are the pit stops for gas and food called "autogrill" and they are not known for their culinary offerings.
If you are not coming back to the area to the south of Siena on your vacation, I'd definitely get off and go through
Montepulciano and from there head to
Montalcino for lunch. From there you can then head up towards
Siena (a brief visit to the center for sure!) and then pass Florence on your way to Lucca instead of heading back to the A1. Assuming you'll be heading to Florence on another day, right?
The other road offers a chance to see the
Tuscan coast. If you will be inland for the rest of your vacation, then I'd recommend taking this road to see this side of Tuscany on your trip up to Lucca.
I'd probably skip Grosseto (it is nice but overall pretty small) and stop in the area around
Castagneto Carducci, another wine growing region in Tuscany. You'll pass lots of villages so stop for lunch wherever something inspires you. You'll find a lot of local trattoria where it is hard to eat badly.
If you want to stop for lunch right along the coast, then I'd stop before. When you are in Grosseto, leave the A1 and head towards
Castiglione della Pescaia or
Marina di Grosseto. At the end of June, you'll have lots of locals around. Another option is
Livorno. Do you like seafood?

Livorno is well-known for their
Cacciucco alla livornese, a seafood soup with tomato and wine served with bread.
If you would like to see a major Etruscan necropoli, you should stop at
Populonia.
You can get more information on the coastal area here:
http://www.costadeglietruschi.it/defaulten.asp
Hope these ideas are useful! Let us know what you decide to do since it gives us more ideas of interesting itineraries to follow in Tuscany.