Superman's wrist watch is at rest with respect to superman. So the time range measured by superman's wrist watch is smaller (i.e. the time runs slower for superman and for his watch) than the corresponding time range measured by Lois on earth. In particular Lois sees superman moving at 0.7c.
There is the argumentation that a watch on earth is at rest with respect to the earth, so that the roles of superman and Lois(earth) are swapped (Superman sees Lois moving). That would lead to the conclusion that the time on earth runs slower than the time measured by superman's wrist watch. It seems actually to be a paradoxon.
However, the situation of superman and Lois is not completely symmetrical, which means that a swap of roles between superman and Lois with its projected consequences on the time advance respectively delay is in fact impossible.
Actually superman not only travels to the space probe, but he also travels back to earth (This fact is extremely important, because otherwise the watch of superman and Lois' watch on earth cannot be compared). Therefore superman's invariant line element is shorter (due to the hyperbolic geometry of the Minkowski space) than the corresponding line element on earth. This cannot be changed by a change of reference system, because the line element is invariant under change of reference system.
The last paragraph is explained now in more detail:
The line element is defined as
$$ (\Delta s)^2 = c^2 (\Delta t)^2 - (\Delta x)^2 -(\Delta y)^2 - (\Delta z)^2$$
in the most general case.
In a reference system on earth Lois has coordinates x=y=z=0, i.e.
$$ (\Delta s)_{earth}^2 = c^2 (\Delta t)^2\quad \text{therefore}\quad (\Delta t)_{earth} = (\Delta s)_{earth}/c = (\Delta t) $$
whereas at superman because he is moving $z\neq 0$, $y\neq 0$ and $z\neq 0$ it is:
$$ (\Delta s)_{superman}^2 = c^2 (\Delta t)^2 - (\Delta x)^2 -(\Delta y)^2 - (\Delta z)^2 < c^2 (\Delta t)_{earth}^2 $$
So the proper time $\Delta\tau = (\Delta s)_{superman}/c$ at superman is shorter, i.e. its time runs slower.
One could now try to change the coordinate system in order to swap the role of superman and Lois. However, the computed line elements for both persons do not change, because the line element is invariant with respect to changes of reference systems.