What Lyric Piece are you referring to?
And I actually found a little Schoenberg that I like to! Except I can't remember the name right now. It's something like 6 Little Pieces, or something like that (printed it out, but it's at home).
There is some Schoenberg that I don't mind such as the Verklaert Nacht, his early Chamber Symphony, and the String Quartet #4 at least. Of course the early stuff is before his serial stuff and to me has somewhat a sense of a late Mahler development section after it went over the tonal precipice. It could also be that over the years, movie music during tense, dramatic scenes often resembles Schoenberg and company so the sound is not as foreign as it once was.
I actually like the Penderecki "Threnody for the victims of Hiroshima", and that really can't be classified as much of anything but ugly. But its purpose was to convey the ugly aftermath of the nuclear bomb. I am also quite fond of the Berg Violin Concerto and the Rite of Spring.
To me, it is not so much the amount of dissonance, it is whether it is used with a purpose. I'm reminded of styles of jazz, not necessarily the wild modern modal stuff, but even ballads where everything is harmonized with some dissonance. The basic harmonic units of jazz are 7th chords (dissonant by nature, all containing a 7th or in in version a 2nd) with the addition of 9ths, 11ths, and 13ths. These dissonances actually give the lushness to the harmonies and we do not necesarily perceive them as "dissonant" (in fact they are often referred to a "tensions")
I'm reminded of some early level students when they run into certain dissonances for the first time. Particularly when they are practicing slowly, it comes out more. They first think that they have played something wrong. Then they try just that, playing louder and louder (I guess thinking that that will make it go away), and then decide that it is wrong. Over the years, I have learned to point these things out on new pieces. I show them that when it is in context at the tempo that we will play that it works. I have them try it out and listen to the sound of the "clash" (and then with the resolution) so they can get used to it and then tell them that if when they practice they don't hear that "clash" then they are playing it wrong.
I'm not sure that art is necessarily intended to always be beautiful. It should be thought provoking and interesting. There is some art in which there is aesthetic "beauty" in the ugliness portrayed. Some of Goya's etchings come to mind where he portrayed ugly scenes about war and did nothing to "beautify" the image.
That of course does not mean that I do not enjoy beautiful art.