The causes of HLHS, and most heart defects are unknown. It could be genetic, or possibly a genetic problem that is triggered by something in the environment. Since you didn't do anything purposely to harm your child, it is certainly not your fault. It is better to focus on how and where your child will receive the treatment for HLHS, rather than worry about the cause.
What are my chances of having another child with HLHS or another heart defect?
According to the American Heart Association, the general population's chance of having a baby with a heart defect is about 1 in 100 that's 1% of all babies born have some sort of heart defect. Those defects can range from very minor things to serious ones that require surgery. Most estimates are that once you've had a baby with a heart defect, your chance increases to about 2-3%. Again, this includes even very minor defects that would not require surgery. Ask your doctor or genetic counselor to discuss your particular situation to see if this is applicable to you.