When I was researching the Lightning for a presentation, I did read that Lockheed designed a P-38 for carrier duty, complete with folding wings, arresting hook and a strengthened undercarriage. The Navy wasn't keen on such a big plane on their decks and they disliked liquid cooled engines for carrier based aircraft. The Navy did fly some lightnings from land bases though. The carrier version never made it off the drawing board.
It's bigger than you think really. If you have stood next to a P-51 or a Spit, then next to a Lightning, it's big!