A heated gas expands and is less dense as a consequence. This is why hot
air balloons fly of course.
The highest possible lifting force due to any lighter than air lifting
method would be from a balloon filled with a vacuum. This would be the
least dense possible 'gas' so to speak.
'Vacuum' balloons have been attempted to be created in the past with no
sucess yet. The container that can hold a vacuum is always too heavy to
benefit from any lift resulting.
What if a pressure could be exerted to expand the balloon from within
yet still maintain the vacuum. Lets say the balloon is made of a
material that has an electromagnetic property that can be acted upon by
a powerful internal electromagnetic field so that it is expanded by
repulsion only. Or we could charge the balloon with electrons which are
weightless until their self repulsion from one another 'fills' the
balloon with a vacuum.
Now lets say we displace a volume of air purely by means of an extremely
intense electric field. The field emanates from a machine. The larger
the volume of air displaced, the higher the lifting force. This would
carry the machine with it. The problem will be that the electric field
will dissipate by ionising the air which will carry the charge away. So
lets make a magnetic field strong enough to attract the ions so that
they remain at a certain distance to act as the balloon 'skin'. Now make
the electric field strong enough to drive all the remaining air
molecules out toward the skin so that a vacuum remains in between. You
might need a 'monopolar' magnetic field so there's no holes in the
'balloon'.