Very few, if any, thru hikers actively fish with the hopes of sustaining on what they catch. There are not a ton of stocked lakes in Southern California that you pass - but once you reach the Sierra fish can be plentiful. But that will require you to stop and spend some time and slow down when everyone else is obsessed with making miles. That much said, if you are going to take time off anywhere, as fun as it was to spend a day in town relaxing, eating and partaking in a frosty beverage, if I had to do it again, I'd take several zeros (zero mileage days) in the Sierra rather than town.
The issue with this of course is carrying enough food to make it possible to take zeros or have very low mileage days in the Sierra. You have to carry a fair amount with you as the distances between resupply points grow larger, so keep that in mind, especially if you are unlucky in the fish department. From what I was told, the fish in the Sierra typically aren't that big.
Once you get through the Sierras and head north, fishing opportunities become increasingly plentiful, especially once you reach the far northern reaches of the state.
In Oregon you pass by a large number of accessible (and stocked) lakes. These are rather easily accessed as the trail goes right by them. In Washington, there are many lakes you pass, but depending when you get to the state, you may be in a bit of a race against time, trying to get done before the weather gets foul.One of the better stretch of easy-to-access lakes is between Snoqualmie Pass and Stevens Pass. Deep Lake is a destination of many fishermen and women; everytime I hike through this area there are at least one or two small groups fishing its waters.