I generally don't. Lyrics aren't all that important they can be absent or totally nonsensical, as long as they don't detract from the music and fit the singers vocal style that's all that really matters.
I guess what's 'good' is subjective, but I personally think a song that can tell a story lyrically and use the music to elevate it like a play is good songwriting. Songs like 'The Boxer' by Simon and Garfunkel, Allentown Jail, Dance of the Dead by iron maiden, Thank You by Dido - are good lyrical examples. It transcends just music to tap your foot to and makes you feel like you're taken into their world and experiencing the journey first hand. Again, that's purely subjective.
There are other more classical examples that are purely instrumental, but there's another thread dedicated to that.
I mean it's more of a sort of "voice is kind of an instrument as well" type of thing. Hell even if youre a singer you kind of think of it that way. I mean lyrics matter but it's more like, nobody writes a song on words alone, even poetry follows a pattern or rhythm.
For me it's not really a thing you can pin down, it's a matter of harmony.
It's really hard to define. Sometimes I like really direct and descriptive songs, sometimes I like really cryptic songs.
Sometimes it's about how the whole arrangement comes together.
I mean The Beatles wrote some perfect pop songs. There's nothing subtle about "Love Me Do" or even a later hit like "Something", but they're pleasing to listen to in a non challenging way. Almost anyone hearing a Beatles song for the first time can enjoy it. The same goes for many country songs- "Give My Love to Rose" and "Mama Tried" are pretty explicit in their subject matter and are better for it.
On the other end of the spectrum you have something like Kimg Crimson's "In The Court of the Crimson King", or 90 percent of psychedelic and prog lyrics where it rides the line between "puzzle-story" and "word salad". It can be engaging to put together the imagery in your mind and try to make sense of it.
Something that feels like it comes from the songwriter's heart and personal experience rather than just a bunch of cliches, the former will often actually be somewhat clumsy and confused but that's the sign of vitality and passion. Husker Du is one of my favorite examples.
"Go to the left, go to the right
Your mind is going to keep you up all night
You twist in your sleep, grabbing the sheets, sweating to death
Sucking on pollution like a rattle in your mouth
You're a big fucking kid, you don't know what you're about
Tell me about your fellow man
You wipe their shit all over your hands"
You can tell this was written by a guy late at night who can't get to sleep, looking outside at the light pollution looming in the night.
I prefer "when I die my seed will be ill like me" from 36 chambers
EDIT: Ghostface in general is one of my favorite lap lyricists, dude never hesitates to get abstract.
"Yo, you fourteen carat gold slum computer wizard
Tappin inside my rap vein causes blizzards"
I have no idea what the fuck that even means but it's badass.
EDIT2: To keep things on topic when it comes to hiphop I love the wordy, intelligent lyrics of late 90s New York stuff ala Wu-Tang, Nas, A Tribe Called Quest, Fugees. They feel simultaneously abstract and molded to fit the beat, but at the same time gritty and personal, like they're creating their own fantasy noir version of New York. "The glock clicked like high heel shoes on parquet floors" from GZA's debut album fucking stunned me.
If elements play into one another to build on the themes of the piece. For example, if piano accompaniment is written so that it personifies something in the backdrop of the song, or the vocal line is written to emulate some part of nature. Conscious decisions being made vs formulaic chord progressions.
If it's something like any type of folk music, to me, it has to feel like it comes from the heart.
If it's something like House music, all you really need is something like "AROUND THE WORLD. AROUND THE WORLD. AROUND THE WORLD. AROUND THE WORLD.", it doesn't need to be deep.
What got me into something like hip-hop was when I first heard Ms. Jackson by Outkast, one of my all time favorite songs. It's got a great, relate-able theme (well for most people, about a cunt of a woman who interferes with their childs significant other), a bit humorous at times, it feels great to hear someone get Blown the Fuck Out that hard, and you can tell Andre 3000 and Big Boi put their fucking souls into the song. There's a reason that song won a Grammy.
Damn OP you actually had to make me think for a minute.