The brightest of all diatonic modes is the Lydian mode. Its best to learn Lydian mode as a modified Major scale which has a raised fourth. For example the key of C is C D E F G A B where as the C Lydian is C D E F# G A B. That raised fourth brings all that extra brightness and colour to a regular major scale so as songwriter, if you want that sound of hopefulness, focusing on that raised 4th note can get that job done. In terms of playing chords, the C Lydian chords are as following:
F#dim * F#min7b5*
Compared to the regular diatonic chords in a major key, we have 3 noticeable difference. The 2 chord which is normally a minor turns to a major, the 4 chord which is a major is now a a raised diminished, and the 7 chord, which is supposed to be a diminished is now a minor chord. Remember the number 247 and that will allow you to figure out the differences between a regular major and Lydian.
The other noticeable thing here would be the GM7. It is supposed to be a v dominant 7th chord but here, the v chord is a major 7th.
The best way to use the Lydian key in songwriting would be to focus on these 3 chords (4 including the GM7) as all of these chords include the raised 4 note.
The theme song of The Simpsons is a classic example used in most music studies. I personally like the sound of II major chord in a major key and beautifully adds that extra hopefulness and positivity to the sound.