Lookout has an often-missed ability to greatly decrease the chance that your other opening buy will miss the shuffle. If lookout turns up T3 then it "rescues" the other buy from skipping if it were going to do so. That, my rough mental calculations suggest, nearly halves the chance of a ruinous first shuffle. If the other card is something epic like Amb, Masq, Steward, Tournament, Spice Merchant, etc then this is a huge plus.
When you play Lookout on turn 3 and your other opening buy is Tournament or Masquerade like you suggested, then playing this card turn 4 will trigger a shuffle which is not the greatest thing because Tournament and your buy on turn 4 (which might very well be a $5er) will miss the shuffle. It's even worse with Page.
Ah yes. A fair point. Maybe this is not as helpful as I'd thought. I'd say skipping the 2nd shuffle is better than skipping the 1st, but I have no idea how the probabilities work out so I'm going to say my comment should be limited to non-drawing openers like Amb, Steward (for trashing), Militia/Cutpurse, Remake, Forager, etc