Aircraft lightning: What are the requirements for airworthiness?
When dealing with lightning protection, there are two significant areas that must be addressed: direct effects of lightning and indirect effects.  

The FAA provides guidance on these two areas in the following advisory circulars:  

20-155A - Industry Documents To Support Aircraft Lightning Protection Certification  

20-136B - Aircraft Electrical and Electronic System Lightning Protection  

The lightning zone analysis from the AC 20-155A will define the test requirements for the airframe and help determine the level of testing for installed equipment based on its location in the aircraft.  

At the aircraft level it can be a very complex and drawn out process negotiating the specific testing required with the FAA. Once that is done, requirements and verification for the equipment can be developed.  A short summary of that process from AC 20-136B is:  


  6. Steps for Showing Compliance.
    a. The following seven steps describe how you may comply with 14 CFR
  23.1306, 25.1316, 27.1316, and 29.1316 requirements for your aircraft’s 
  electrical and electronic systems:
  (1) Identify the systems to be assessed.
  (2) Determine the lightning strike zones for the aircraft.
  (3) Establish the aircraft lightning environment for each zone.
  (4) Determine the lightning transient environment associated with the systems.
  (5) Establish equipment transient design levels (ETDLs) and aircraft actual transient
  levels (ATLs).
  (6) Verify compliance to the requirements.
  (7) Take corrective measures, if needed.
   b. The steps above should be performed to
  address lightning transients induced in electrical and electronic
  system wiring and equipment, and lightning damage to aircraft external
  equipment and sensors that are connected to electrical and electronic
  systems, such as radio antennas and air data probes. Additional
  guidance on lightning protection against lightning damage for external
  equipment and sensor installations can be found in SAE ARP 5577.  


Testing of individual LRUs is typically under RTCA document DO-160G - Environmental Conditions and Test Procedures for Airborne Equipment.  Section 22 covers Lightning Induced Transient Susceptibility and Section 23 covers Lightning Direct Effects.