Took an Idea off Pinterest to Hang a Bed ( Single Mattress ) from the Ceiling using 4 Chains located in the Backdeck Sunroom... The Basic Weight or Stress Factor if you will aside from the chains will be a platform made with 2x4 & plywood and mattress of course... My Intensions are to screw in a 2x4 cross member into the ceiling from stud to stud to that... Then screw in hook lag bolts to hang the chains off.. Hence my Question, Will the Lag Bolts Hold the Weight and if so How much Weight?

Lag bolts aren't all the same size or length, not al lumber is equal either they will be screwed into. Plus its unknown how much weight is acutally on the ceiling studs to begin with because of span, what all is above it as wel as the thickness of the sheetrock, how the roof above it is built and what weight is being born on those.

Lots of unknowns. I also assume you own the house this will be done and aren't renting... and that this isn't an apartment or condominium where those studs are part of the common and not actually owned by you.

Asside from all that, if you are talking a single lag bolt to hold everything....I would highly recomend against it because lag bolts are typically the lowest rated bolts, meaning they are soft and not extremely strong on their own individually.

I would never use lag bolts in that manner. If you have access above the ceiling use thread screw eyes and large fender washers. However, both of them are marked on the tags against your proposed use.