Lively Jitterbug coverage used to be provided by a patchwork network made up of a whole slew of carriers. My Jitterbug J originally came with a Qwest sticker on it. However, coverage is now provided by Verizon.
Verizon's network is, of course, very good. This Jitterbug coverage page lets you check your zip code, but it doesn't give you a street-level map. For that you would have to head over to Verizon's website.
In any case, I have personally found the coverage to be very good up and down along the East Coast and in the Mid-West.
On the old Jitterbug phones there were a couple of ways to know whether you had a good enough signal.
The quick way was to just flip open the phone and check if there was a dial tone. If there was, then you could make a call. Simple.
The other way was to go to the "Phone Info" section of your menu. There, the actual signal strength was given as either good, fair, or poor. All these levels still appeared to be strong enough for making calls. I don't know if these options are there on their current phones.