A number of Apollo designs proposed a lenticular command module. Not an "aircraft," more of a spaceplane to be sure!
The problem with a lenticular aircraft is stabilizing it; you need some kind of tail fins, which detracts from the purity of the perfectly circular planform. You wind up with basically a delta wing with a rounded leading edge.
The Vought "Flapjack" concept took advantage of the very high range of lift coefficients available to a wing that has a very low aspect ratio (ie, low span compared to the chord), the large area of a flying-wing concept, and using the propellors to counter the high-drag-producing tip vortices, as well as using prop thrust for lift at high angles of attack, to produce a very Short-Take-Off plane that would lift off the ground at a very low airspeed (hence very short take-off run) and then perform well at high speeds. Note that it wasn't properly circular in planform either--more of the
back of an elongated ellipse. It achieved a decent moment arm for the flaps to work on by the ellipse being longer than wide, so cutting it in half left a decent arm still to work with.
There's no good way to adapt the concept to jet propulsion though, since it relied on the swirling of the props to counter the swirling of air flowing from the high-pressure bottom of the plane to the low-pressure top, which phenomenon is responsible for "induced drag" that is the main source of drag at low airspeeds.
The usual way to deal with induced drag due to tip vortices is to make the planform of the wing very wide--span of the wing is normally much longer than the chord, the length of the wing fore-and-aft. This reduces the percentage of the wing area that is undergoing the swirling, it reaches the extreme in sailplane designs which have very broad, very thin wings.
Such designs tend to stall very easily though.
Going the other way, making a wing that is longer than it is wide, means that at a given lift coefficient--which is a ratio of the lift you get to the wing area--the induced drag is higher, however due to some actually useful properties of the swirl, stall is delayed and moderated, so a delta-winged plane can go to a very high angle of attack, getting a much higher lift coefficient; combined with the large wing area this means you can get good lift at low airspeeds, paying a cost in high drag there to be sure, but with lots of thrust you get off the ground at lower speeds. Then when reaching cruise speeds, the high wing area means a penalty in drag area, but this is offset by "burying" a lot of the normal features of an airplane in the wing, and the large wing area means you can cruise at lower lift coefficients that offset the higher drag at a given lift coefficient.
Deltas are especially good for supersonic flight since the wings are well-swept and can be given sharp leading edges. For a strictly subsonic delta, you'd want the angle lower and the wings broader, and this gets into the territory where the length is low so the moment arm for pitch control is low--getting in fact into the territory of the Northrop Flying Wing, which had serious problems in that respect.
That's the realm where you'd want to look at circular planforms, but a shape that is symmetrical fore and aft will tend to be unstable and pitch crosswise to the airflow.
The spaceships being lenticular were an interesting and perhaps clever compromise for a craft meant to straddle a very broad range of aerodynamic conditions, from hypersonic orbital (or, for Apollo, return-from-Lunar, which is practically the same as Earth escape velocity) down to a landing at airspeeds hopefully measured in less than 100 knots, or at any rate not much more than that. Like other spaceplane proposals, the idea is at very high entry speeds to go belly-forward, to achieve maximum braking and get rid of that excess speed that otherwise would roast the craft and then melt and burn it up!

Then the tricky bit is, how, from a craft that can handle that, can you get decent aerodynamics at low supersonic and subsonic speeds? A lot of space experts seem to be coming to the conclusion that the simple ballistic capsule, that basically gets very poor aerodynamic performance as an aircraft, is really the best way to go. A spaceplane is tricky. The Lenticular ideas seemed to rely on the concept that while a lenticular aircraft is not fantastically good as an airplane or glider, it can be made to work well enough, whereas it is a good form for hypersonic entry, belly-forward that is, and mechanically it can offer some simplifications over normal airplane shapes that allow for weight savings.
It looks clever and certainly cool for a spaceship. One notes though that no one has ever done it, and perhaps never will.
Again, for sheer wacky flying saucer madness, check out the
Bono Saucer, which is again a spacecraft--this time not a manned capsule but a whole reusable very heavy lift booster. (Upon consideration it seemed obvious the goals could be met in a more efficient manner, so the idea was shelved, but there it is--not so much a "flying" saucer as an orbiting one! And massive!)