The bill has already been made. It was tabled in the House of Commons. It then has to go through three readings, which it has. After that, it is sent to the Senate. If the Senate doesn't make any changes it then passes to the Governor General (the Queen, if she's in country, which is very rare) or a deputy, who signs it into law.

If the Senate modifies the legislation, it is then passed back to the House for review. If the Senate chooses to vote against this legislation, it dies. Both the Liberals and the Conservatives have used their majorities in the Senate to kill legislation the other party has passed before.

The interesting thing about this piece is that Harper will probably allow a free vote in the Senate, meaning it is possible that the Senate could pass it. Given that there's so much pressure on the Senate these days, I wouldn't be surprised if the Senate just let this one through untouched so as not to raise public ire.

The lieutenant governor is only the Queen's representative on the provincial level. They have nothing to do with federal legislation. They also rarely review legislation. As the monarchy's role is generally ceremonial in nature, it would be quite shocking for a viceroy to have any say in legislation, or even to reject passed legislation.