Cuthbert has been out since tearing his hamstring in Wales' RBS 6 Nations title victory over England on March 17 and was expected to return for Cardiff Blues against Ulster on Friday only to be withdrawn just prior to kick off.
But the 22-year-old insists he will be fighting fit for the Lions' tour opener against the Barbarians in Hong Kong on June 1.
"It was just a pre-caution," said Cuthbert. "Phil Davies decided I should not risk it and it was probably a sensible idea because there was nothing much on the game.
"The rehabilitation has been going well but it is important I don't rush things with such an important couple of months going up."
North, 21, was withdrawn by Scarlets coach Simon Easterby on Friday having reported breathing problems, but is expected to be fit for the Llanelli outfit's Celtic League semi-final with Ulster in Belfast this Friday.
"George has trained this week - he's pretty good," said Easterby.
"There are a few sore bodies and we will probably wait until Thursday before naming our team."