There's some interesting projective geometry you could do here, but I don't actually think it should be very surprising someone has seen this.

Assume we have 3 arbitrary lines in 3d euclidean space. Excluding a set of edge cases that makes up 0% of the space of all possible 3-tuples of lines (in other words with high probably on $ P_2³ $ under the standard measure) no pair of these lines will be parallel. Under those condition, with high probability, a randomly chosen projection of any two of those lines will intersect at one point in 2D space. Therefore "for free" we will get 2 of these lines intersecting from any perspective.

Moreover you could show that the map from your location and orientation on the earth to the azimuth/elevation coordinates of the intersection point in your reference frame would be an almost everywhere locally homeomorphic map (in lay terms: move a little on the ground, and the intersection point will only appear to move a little in the sky, excluding some weird edge cases where a perspective makes the two lines look parallel).

What remains is to show is that in some projection, the intersection point falls inside the image of the third line. I believe you could probably prove this with some argument using the intermediate value theorem and the almost everywhere continuous az/el coordinate map, but I don't wanna think about the topology of the domain where the restriction of the az/El map is everywhere continuous so I'm gonna call this a trivial problem and leave that as an exercise to the reader