Is there a special spanner I can get for a headset lock nut or do I just use a large adjustable spanner?
you can
i have one, however it was weak and a bit out of sizing and put marks in the nut (cheap bike tool)
i then used a shifter with greater success
Whats a shifter!?
For the top nut, an adjustable spanner (a.k.a shifter) is fine - though you would usually use headset spanner to hold the lower cup still while tightening. With a bit of trial an error you can back off the cup a little and allow for it to tighten if you are just tightening the top nut. If you have a notched streerer and matching tabbed washer, you should be fine.
That’s a right handed one. 
aren’t you cute
Not really…just a retarded pom.