Bowser has a massive shield to mitigate projectile spam. One of his best approaches is to just dash at you and power shield when appropriate. When near, again, the shield comes into play against X attack and then any number of follow ups are possible: Grab, Klaw (the other grab), Fortress, Jab, FTilt, Jab Cancelled Grab, whatever.
Couple things about this - It's great that you have a big shield - but Lucas amazing at countering shield with nair, and it's pretty hard to stop, and no, it's not as simple as just shield grabbing us. Lucas will move behind your grab range through your shield fast enough to stop that. Most Lucas players WANT opponents to just throw up their shield, it makes things rather easy for us.
Another good approach is Klaw Hopping which is very unprdictable. Klaw itself is disjointed when airbourne and has a landing lag of only a couple frames. Plus, it's a grab. So when you play Bowser, watch out for both of them.
In the video, when NL would Klaw Hop, the Lucas kept attemping SHPKF's, which isn't the way to go against Bowser. One FHPKF would have taken care of those mind games, and the wave bounce coming from FHPKF's is huge, and can also be magnet pulled afterwards creating ridiculous Lucas trajectory making him extremely hard to punish for this action.
While NL pulled the stunts in that match about what Bowser can do to Lucas, that mediocre Lucas player at best showed nothing about what Lucas can do to Bowser. :\