I don't know for sure but I suspect you're on your own. You're certainly expected to make your own way from LHR to LGW, with your luggage, at your expense. The fact none of the LGW routes are available as options if you select EDI as your start point suggests they're not considered connections which would be honoured in the event of problems.
But you never know - that might not be the case: try calling them. Even if they're not legally obliged to rebook you on to a later flight in the event of a delay VS will normally do what they can to help if things go wrong. Failing that, would your travel insurance cover you?
I'd allow 4 hours between your LHR arrival and LGW departure to be safe - bag drop at LGW will close an hour prior to departure and VS recommend you're there 2 hours prior.
As an alternative have you considered the VS flights to Orlando from Manchester? There's a direct train from Edinburgh to Manchester Airport at about 7.45am which connects with the VS73. It takes about 3.5 hours but by the time you've schlepped round the M25 from LHR to LGW you'll save time, not to mention hassle.
