This year is the 400th anniversary of the printing of A Musicall Banquet. It's a collection of songs compiled by Robert Dowland, son of John. Inside the collection are 3 songs by John (Farre from triumphing court, with words by the formentioned Sir Henry Lee, Lady if you so Spight me, and In darknesse let me dwell), a bunch of songs by guys who were otherwise not known to be songwriters (Anthony Holborne, Daniel Batchelar and Robert Hales, who was Elizabeth's favorite singer and sang the formentioned His golden locks at its premier). It's also got a number of French airs de cour, some Spanish songs and some Italian, including Caccini's Amarilli and Dovro dunque with written out lute accompaniments instead of just figured bass.
The poets are given credit as well in a lot of cases. There are some by Elizabeth's lover, the Earl of Essex, and some of the 'Songs' (as opposed to sonnets) from Philip Sidney's Astrophel and Stella. One of these Sidney songs, In a Grove, was written to a pre-existing tune by Guillaume Tessier. Tessier's air originally set a poem by Ronsard, so Sidney is imitating French poetic meter just by using the tune as a model. (I've linked the poems so you can compare if you are skilled in the French tongue.) Sidney did this in other places in his Certain Sonnets collection.
If the embedding above doesn't work, you can download a (free) mp3 of a live performance of MIO singing Change thy mind, words by Robert Devereaux, Earl of Essex, music by Richard Martin, (not the same guy as Livin' la Vida Loca singer Ricky Martin) here. As I say, it's live, so please excuse any performance bobbles, the subway noise and the truck that goes past. The text of the poem is here.