Moorhead was six under par through his first eight holes, but mixed a couple of bogeys with just the two more birdies to finish at minus six.
Lee drove the par four 7th hole and made eagle to get to five under, but two bogeys with three more birdies also had him at minus six.
He was coming off the back of his impressive win in the Eketahuna Masterton pro-am at the weekend, where he took the honours by two shots from Daniel Pearce (Ashburton) after shooting a record-breaking 63 at Lansdowne on Sunday.
Pearce, for his part, also continued his good form at Martinborough, finishing in a tie for fourth after a round of 68. Leading scores at Martinborough:
62 Andrew Henare (Hastings)
66 Richard Lee (North Harbour), Grant Moorhead (New Plymouth)
68 Joshua Carmichael (North Harbour), Daniel Pearce (Ashburton), Dominic Barson (Kaitake Golf Club)
69 David Klein (Te Anau), Keiran Muir (Omokoroa), Bryce Mawhinney (Manawatu), Craig Hamilton (Omanu)