This, of your three choices would be correct: "Is A more lightweight than B?"
If you look up the meaning and usage of "lightweight", as shown here...
light·weight /ˈlītˌwāt/ noun (from Google dictionary)
noun: lightweight; noun: light-weight
- a weight in boxing and other sports intermediate between featherweight and welterweight. In the amateur boxing scale it ranges
from 125 to 132 pounds (57 to 60 kg).
• a lightweight boxer or other competitor.
plural noun: lightweights; plural noun: light-weights
- a person or thing that is lightly built or constructed.
• a person of little importance or influence, esp. in a particular
"he was regarded as a political lightweight"
adjective: lightweight; adjective: light-weight
- of thin material or build and weighing less than average.
"a lightweight gray suit"
- containing little serious matter.
"the newspaper is lightweight and trivial"
..."lightweight" is a noun or an adjective. In your first example: "Is A lighterweight than B?", your combined word "lighterweight" does not make sense. Since it, like "lightweight" would be a noun or adjective, try replace it with a noun or adjective to test for accuracy. Would either of these sentences make sense to you?
Is A book than B? or "Is A awesome than B?"
What you want to know is whether or not A weighs less than B so you must keep "lighter" and "weight" separate as their own words:
"Is A lighter weight than B?", or as you already proposed, "Is A more lightweight than B?", making "lightweight" an adjective in that example.