The algorithm has three subalgorithms: maximum connectivity graph, minimum connectivity graph and interpolation between minimum and maximum. Don't get discouraged by the word graph, I won't dive too deep in graph theory mathematics, I'll just as a convenient word for "a way how points are connected with lines".
The general idea is to start with maximum connectivity and remove connections until desired starlane density is reached. Maximum connectivity algorithm has been the hardest part to nail down. I've tried and scrapped about a dozen methods. First couple of ideas looked promising until I've run into edge cases which were impossible to handle without introducing some undesired properties like bias toward topmost or leftmost star positions. Then I've tried to get so called Delunay triangulation working. Failing to find easy to copy-paste code and after contemplating whether it's worthy or not to spend time integrating nontrivial code I have found, a simple solution dawned on my mind. I figured my ideal solution would always contain shortest possible connection and from there I assumed the ideal would favor short connections over long ones. I expanded it to an algorithm which checks potential connections one by one, from shortest to longest, and adds a connection to a solution if it doesn't cross over previously added connections. Prototype was promising, there was only an issue where some points had a lot of lines coming out in a narrow cone. After adding a condition where a connections has to have certain minimal angle between them I solved that issue and got satisfactory results.
Minimum connectivity algorithm starts from maximum connectivity solution and finds the smallest set of connections necessary to connect all points. First it picks a point closest to the center and adds connections which form a shortest path from player homeworlds to that point. That central point is momentary substitution for what will later be a stareater's "brain" system so this steps ensure that players will have access to it and to eachother (and shortest path ensures there will be no cycles meaning no superfluous connections). Then the rest of points unconnected by those paths are added to solution by taking the shortest connection which would connect a new point with the set.
Finally, depending on chosen starlane desnity some extra connections are added to minimal graph. Again, the shortest candidate connections are added but this time the ones linking points with least connection endpoints have a priority.
All this was accompanied with some general map generator code refactoring. Parameters (map size, position randomness, starlane density) are handled in a much nicer way and last map settings are finally getting remembered. Now that I think about it last number of players is still not remembered, oh well. Anyway, the map still has to be filled with stars and planets in some meaningful way, I have some ideas and I'm look forward for a day when third piece of the puzzle will fall in place.