If you’re playing in Lydian mode in C major, the ‘home’ chord would be the IV or F major tonic. You can also use E minor and G major to centre around the F major. You will need to be able to use your ear to pick chords that resolve to the centre ‘home’ chord. You need to decide what are the best chords to compliment and draw towards your home chord as the centre. You want to pick chords that can draw away from the tonic but not too much to the point where the centre is lost. You want to pick chords that reinforce the tonal centre (chord).
This can be tricky for some chords such as iii – Phrygian and vii(dim) – Aeolian because they naturally sound unresolved.
Here is a list containing the chords that reinforce the tonal centre in each mode taken from this website.
- Ionian I, ii, V
- Dorian ii, iii, ii, V
- Phrygian iii, IV, iii, ii
- Lydian IV, V
- Mixolydian V, ii, V, IV
- Aeolian vi, IV, V
It seems to be a trend that other than ionian mode, the other modes do not contain the tonic of the parent key’s chord and that would be because it is so strong that it would totally draw the tonal centre away from the mode being used. The V chord is used quite a bit and that would probably be because it is the dominant of the parent scale and not enough to draw the tonal centre away.
These trends are kind of reflected in this graph above taken from this website which analysed the most common chord progressions in pop songs.