Okay, lucky or just bad or both? Good question. Lightning draft picks that stayed with the org and became regulars / core players for the Cup runs and after:
2007 3rd round: Killorn (77th)
2008 1st round: Stamkos (1st)
2009 1st round: Hedman (2nd)
2011 2nd round: Kucherov (58th)
2011 7th round: Palat (208th)
2012 1st round: Vasilevskiy (19th)
2014 3rd round: Point (79th)
2015 3rd round: Cirelli (72th)
2017 6th round: Perbix (169th)
All other relevant pieces were acquired via trade or FA signing. And the other picks have been total busts and/or were shipped out in trades.
This list is actually incredible, 9 of our 20ish guys on the cup team going back 13 or so years were still here. When you include non-drafted free agent signings that list is significantly bigger. Johnson, March, Verhague, Gourde, etc. Those hits have been replaced with duds like ABB. Huntington.....
We also had tons of role players during that span who contributed to some seriously good teams. They may have been replaced, but other than the Cups we've had plenty of success over the last decade.