One way to make that ordering work with Lydian is to start with Lydian and flatten one note each time. So say we start in C. C lydian, flatten the F# we have C Ionian, flatten the b we have C mixolydian, flatten the e we have C dorian, flatten the A we have C aeolian, flatten the d we have C phrygian, flatten the g we have C locrian

Now we flatten the C (after all this is the next note in the cycle of fifths) and we have.... B lydian. And the whole thing starts again.

In this way you can understand how all the modes and keys relate. You can do a similar thing with the other 3 similar modes of limited transposition in this order (melodic minor, harmonic minor and harmonic major).

Have fun.