In your question you are probably implicitly asking what will be one – way speed of light between the spaceships in their "moving" frame (in the direction of their travel or in opposite direction) and whether its value will be lesser or greater than $c$.
It is allowed to assume, that in the frame of these spaceships one – way speed of the beam is lesser than $c$ in “forward” direction and greater than $c$ in “opposite” direction.
But, if the astronauts would measure speed of light on a closed path using a single clock, the measured value would be equal precisely to $c$ in any direction anyway.
Lorentz Ether Theory admits that motion is absolute, but relativistic effects make it undetectable. This theory assumes that there is a preferred frame. Speed of light is isotropic only in preferred frame. In a moving frame speed of light is anisotropic, since this frame moves in a preferred frame. Clocks of moving obsrvers indicate so – called local time, which is different from absolute time.
This theory is empirically equivalent to Special Relativity. Special Relativity assumes, that there is no preferred frame and one - way speed of light one - way speed of light is isotropic an equal to constant $c$ in any frame.
It should be noted, that it is not possible even in principle to measure the one way speed of light. So, equality of speed of light in different directions and Einsten's method to synchronize clocks is a convention, which looks natural only in inertial frames. In rotating frames, even in special relativity, the non-transitivity of Einstein synchronisation diminishes its usefulness.
Reichenbach‘s synchrony convention allows anisotropic one – way speeds of light, but keeps average speed of light on closed path isotropic and equal to constant $c$.
Let‘s assume, that the spaceships move at equal velocities very close to $c$ and chase each other in preferred frame or Ether, so distance between them doesn't change. In the frame of these spaceships "real" speed of light between them will be different from $c$, because they also move with speed close to $c$.
From the point of view of an observer who is „at rest“ in the Ether, difference of velocities will be $c-v$ or $c+v$. But, it is necessary to keep in mind length contraction and time dilation. However, since astronauts do not know anything about their own movement, measured speed of light in one direction will depend on their clocks synchronization method.
If the astronauts compare round – trip speeds of light in different directions, they would measure, that roundtrip speed of light is isotropic and equal $c$
(Michelson - Morley experiment).
Since the astronauts know nothing about their velocity, they may ascribe value $c$ to one - way speed of light and synchronize front and rear clock accordingly. This way, due to discrepancy between the front and the rear clocks (they would show not “real absolute”, but “wrong local” time) it is clear that measured one – way speed of light will be equal exactly to $c$.
However, if somehow the astronauts at some instant were able to set time on the front clock and rear clock according to „absolute Etherian time“ they woud give different values for one – way speeds of light.
In forward direction it would tend towards $c/2$ and in the backward towards infinitely large value, so measured speed of light „back and forth“ will still be $c$.
Chapter: Generalizations of Lorentz transformations with anisotropic one-way speeds