Newton's Third Law and Net Force

The question is unclear. Perhaps you might want to include all the forces in including gravitational force and then reformulate the question.

Nevertheless, let me provide a complete picture of the earth and rocket system.

We have an earth that exerts a gravitational force on the rocket $F_{e-r}^g$ and by Newtons law the rocket exerts an exact equal but opposite in direction force on Earth, $F_{r-e}^g$ such that $F_{r-e}^g=-F_{e-r}^g$. Furthur we have the lifiting force of rocket exerted on earth $F_{r-e}^l$ and the reaction by earth on the rocket $F_{e-r}^l$, such that $F_{r-e}^l=-F_{e-r}^l$.

Now the net force on rocket is given by $$F_{rocket}^{net} = F_{e-r}^l-F_{e-r}^g$$ Here the upward direction is considered positive.

The rocket will have no net force if $F_{rocket}^{net}=0$ which happens when $F_{e-r}^l=F_{e-r}^g$. The rocket can accelerate/decelerate by varying $F_{e-r}^l$ which effects the $F_{rocket}^{net}$ by the relation shown above.