You cannot access the header using Lambda. But what you can do is to create a display template in Api Gateway that places the header value in the event object.
The header must be in a variable $input.params(x)that can be used in the mapping template. See the full documentation on how to integrate this accurately.
update: in the mapping template (under api gateway -> your endpoint -> integration request) add something like this:
#set($inputRoot = $input.path('$'))
{
"apikey" : "$input.params('X-Api-Key')"
}
Now you can access the api key in the lambda function under event.apikey(I have not tested this, but we use something similar in production). Please note that you can do this for all header variables as well as variables in the body.