I think what you have in mind is not so much a lifting body as a bullet fairing. And they have been used on a lot of hydrofoils as well as aircraft.
A lifting body by itself is very inefficient because of its small span. But in conjuntion with the rest of the foil, it may help to provide carry-over of the lift distribution so you don't have such a dip in the spanwise lift distribution as you would have with an axisymmetric body as the fairing. So I would tend to make it look more like a blended wing-body in shape and design philosophy.
I think there's a lot of merit in adding volume at the joint to provide structural strength and room for control mechanisms. I've taken a first cut at such a fairing, as shown in Figure 22 of my
Basiliscus paper. The idea of these fairings was to area rule them in an attempt to reduce the local increase in velocity in the junction between the foils, especially when the foils joined at an acute angle.
If you consider an axisymmetric shape with ogive nose and tail, and cylindrical centerbody, you get a somewhat dumbbell-shaped pressure distribution that has a maximum velocity near the joints with the cylinder. If you neck down the centerbody so the body is dumbbell-shaped, too, you get an even more pronounced set of low-pressure peaks and an increase in pressure in the center.
Now consider the flow in the junction between the hydrofoil and strut. There is an increase in velocity (decrease in pressure) near the maximum thicknesses, a stagnation line along the leading edges (high pressure), and an increase in pressure at the trailing edge. The velocities due to the thickness distributions of the two foils add together near the joint to exaggerate the high-speed/low-pressure region, leading to a lower incipient cavitation speed and steeper pressure increases to the trailing edge that promote boundary layer separation.
These effects can be partially cancelled out by adding a dumbbell-shaped body that is sized so that the low-pressure peaks correspond to the high-pressure regions at the edges of the foil and strut, while the high-pressure region in the middle overlays the low-pressure region in the joint.
The final shaping of the fairing was done by pinching the aft end to flare it out into concave fairings with sharp trailing edges, but which still maintained the increased volume of the dumbbell near the trailing edge. This was done specifically to try to maintain the lift through the junction as you suggest.
I've not done much CFD work, yet, to see how well this concept really works and to optimize the shaping. But I think it has some promise.
