In fact, we can draw gravitational force field lines in the way that one draws magnetic and electric force field lines. In practice, we rarely, if ever, do so. That is due to a combination of convenience and, to a lesser degree perhaps, to the historical development of the subject.
For an isolated point mass -- a good approximation external to a radially symmetric object such as a planet -- the gravitational field lines would be straight lines radially outward from the centre. The density/concentration of the lines decreases with the square of the distance. That would be the same form as for the field structure of an isolated electric point charge.
In most gravitational situations -- e.g. rocket launches, orbiting satellites -- we have a small object being gravitationally attracted to a single, isolated large body. We could, in such a situation, draw the gravitational field lines. However, of greater interest is the path/orbit of the small body which is determined by the simple rules which govern projectile's trajectories and orbital motion (Kepler's Laws). There is nothing to be gained by drawing the lines of force.
For an object moving within the combined gravitational fields of two bodies, e.g. gas particles within a binary star system, the field line structure is not drawn because there is a much simpler and more useful way to map the gravitational field: we draw surfaces of constant gravitational potential. Those surfaces are analogous to elevation contours on a topographical map of the Earth's surface. By looking at those contour lines, the labelled values, and how close together they are, we can readily deduce the ease with which we (or any other 'particle') could manoeuver through the field, and the direction which a free particle would fall.
We could represent the electric field for a distribution of electric charges, or the field for a magnetic dipole, say, with a map of potential surfaces. Indeed, that is sometimes done. For the magnetic field of the Earth, however, the magnetic field lines are intuitively more informative: They immediately tell us the direction in which a compass needle will point at a given location in space. On an equally mundane level, sprinkling iron filings around a magnet immediately reveals the field line structure. We cannot do the equivalent with a gravitational field.
In summary, we could map a gravitational field with lines of force as we usually do for electric and magnetic fields. However, we don't do it, because it is not as useful as when we do it for electrical or magnetic fields.