Lobbying Cabinet and federal independent agencies is very similar to lobbying congress. Please follow the link below to see my quick guide on that topic.
There is however one huge difference. Cabinet level and other federal agencies are issue experts and they work for the president of the United States. The person who holds that office has a set of priorities. He or she will use the power of the presidency to execute laws passed by congress in ways that align with his or her priorities and beliefs. In short, you have to know the political terrain, i.e. what the president wants to accomplish, and you have to know that you are dealing with really smart dedicated people who want to help the president succeed.
Building connections to federal officials is key. Generally speaking, if you lobby congress you will come across people who work for federal agencies. They are lobbyists too, but for the United States and more specifically, for the president. They will work with congress on legislation to ensure that what is passed is in some way something that the president can execute. Federal officials know the members of congress who have jurisdiction over their portfolios and work very closely with them.Can you ask members of congress to help with federal officials? Of course. I spent an entire year working as a liaison for a member of the senate to federal agencies. Lots of people asked for my help in making connections and I helped out where I could. Definitely use your legislative contact to help when working with federal agencies.
What else can you do? Two things: know the executive branch rules (see below), and become an expert in the issues that you are working on. Regulatory lobbying is very technical. You need to be an issue expert as well as and expert in the administrative procedures used to enforce the laws. There are many books and courses on the federal rulemaking process and I have provided a couple of links below.