Absolutely a combination of both.  Let’s first look at the lifting portion of this with an example.

Let’s say you’re max split (lowest you can get, and I’m just making numbers up here mind you) is 1:30/500 meters.  To hit your 6:56(going to use 6:56 for even math) you need a 1:44 split which is 64.79% of your maximum output.  If, through lifting (which is going to affect your maximum output the most) are able to get your maximum output split to 1:27, to hit that same 1:44 you now operating at 58.53% of your maximum output.  You’ve essentially made that 1:44 7.26% easier to handle.  

From a steady state standpoint you can train your VO2 max, to improve your performance (essentially more steady state is going to allow you to use more oxygen during a test).  If you are used to doing steady state at say a 2:05 for an hour, through erging and training, you are able to then hold a 2:02 for an hour of steady state (and still stay in the appropriate heart rate ranges) you have improved your ability to hold lower splits by improving your efficiency.  Again, you essentially make that 1:44 more obtainable by being more efficient with your oxygen usage.

Long story short - lift, erg, win.