Trajectory generation is a fundamental part of planning for lighter-than-air robots. In the first part of this paper, the accessibility of this nonlinear affine system with drift is studied using the Lie algebra rank condition. The second one presents 3D time-optimal translational trajectories characterization for a lighter-than-air robot in steady wind. If unaccounted for, winds can substantially degrade the performance of an autonomous airship guidance system. The minimum time problem is considered using the optimal control theory to establish the 3D path between two different configurations (position and orientation), assuming that the system has independent bounded control over the acceleration as well as the turning rates for the flight path and heading angles. The contribution of the work is to do the planning in 3D with varying velocity, heading angle, and path angle, taking into account a piecewise constant wind, with a periodic update.