The song is in G Lydian in the sense that all the notes are from the G Lydian scale (which is actually the exact same notes as in a D major scale).
But the program does not emphasize the G Lydian tonality by hitting that #4th.
But if you create a G Lydian song, use a chord progression with a lot of 1's in it and avoid the 5, and maybe even use chord separation and pads I think you will get quite a few good sounding G Lydian compositions. What I usually do is create 10-50 songs, then click through them to find something I like then build upon that.
I feel that part of the reason for using a program like this is to get inspiration, and a big part of that is going 'outside the box' so to speak. So the flexibility regarding mixing of scales, modes, progressions and structure is an intended feature, not a limitation.
That said, I hear you, and it is actually a good idea to have some kind of 'style templates' that the user could select from. I will put it on my todo list as well.