Virtually all diesel engines require a lift pump to get the fuel from the tank to the high pressure pump and into the engine. There is a noted oddity in recent history, that being the Duramax engine from GM. From its introduction in 2001 through 2016, it didn't have a lift pump (this is news to me too!). What makes this strange is, the injection pump on the ...
I had a friend have this issue and kept going into limp mode and I found her connector for the knock sensor was faulty and losing connection and when it did it would run horrible and even die out and have a hard time starting, I rewired the connector and it solved her issue.
Here are what these codes mean:
P1336: P1336 Description
P1339: P1339 Description
I cannot imagine any connection to the fuel injector. It's best, IMHO, to assume that the codes are accurate and follow that until you prove otherwise.
Most likely you have some wiring problems. Find a better mechanic!