Any thoughts on having Lucerne as a base for 2 weeks in July with a car?

That depends on your expectations. Do you just want to relax and see the area around Lucerne? If yes, then it should be fine. You can take daytrips to Lugano/Locarno and BO as well.

Personally, I'd stay in Weggis rather than Lucerne for a more relaxed feeling.

If you would like to see Zermatt and Engadin, then I would advise having 2+ bases in Switzerland.

Schuler, the advice on staying at Weggis instead of Lucerne was GREAT for us. It was very, very convinient. As you tell Virginafish, it was very relaxed and quiet. Sunsets by the lake were divine!

Parked the car in the hotel and never moved it for four days.

We drove thru Lucerne, and the traffic was hell. Also recommend staying in Weggis. The Seehotel Gotthard was nice, reasonable, free parking, and right on the lake.

I have been recommending Weggis (and Vitznau) for years over Lucerne. Much more charming towns, better lake and Alp aspects, no crowds (esp. day-trippers, no traffic). However, I would not base myself anywhere for 2 whole weeks and try to “see” Switzerland from one place; it’s simply too much traveling IMO even fro such a small country. You have 2 weeks, you should move at least once. Consider the Lake Geneva area. Agree on the Engadine as well as another place to consider staying for a few days. There is no point in spending all your time in a car, you will get tired of driving on the same roads all the time.