The Scot has moved into the transfer market to land Millwall defender Whitbread and Stockport striker Johnson for undisclosed fee and the duo have penned two-and-a-half year deals.
Lambert said: "Zak is someone I've been after for a while and he is an experienced defender. He has always been my first choice and I'm delighted to bring him in.
"Oli is an unknown quantity but he will give defenders a real fright. He scored six goals in his first nine starts for Stockport and he is not long out of non-league."
Meanwhile Lambert has also distanced himself from reports linking him with the vacant Burnley job. "I'm not going anywhere, he added. "I love it here. I've got a great rapport with people here and I'm not going anywhere."