This word uses the kun'yomi readings for the kanji. You kind of learned this reading for 憂, but not exactly. Here's a mnemonic to help you remember it:
The bitterness that shows in your eyes takes the rays (れ) of light out of them, leaving you with just the う part of the reading that you know. That's why this reading is just う and not うれ like the others.
I met with the misery of a broken heart.