Please list for me the two famous and best poems by D.H. Lawrence.
This is one of those questions which can and should receive a variety of responses for two reasons. First, there is no definitive list of Lawrence's poetry (or most poets, for that matter) in order of best to worst; the closest you might get is most popular to least popular. Second, poetry is personal, and what one person responds to may not impact another. The best I can do for you is give you the two Lawrence poems I most appreciate.
One poem by D.H. Lawrence which I like is "Listening." Two lines in the first stanza always captivate me:
I listen to the stillness of you,...
I feel your silence touch my words as you talk.
The poem uses amazing imagery which appeals to all senses, and the most impactful image is that of a forge. It conjures up all kinds of things: sparks flying, the sound of metal on metal as well as the whooosh of the bellows, the heat, and the movement. Ironically, all images which are anything but silent. This is a poem about living in the world but also rising above the mad crush and noise of the world and listening to the silence.
My second choice is "The Piano." While I enjoy the poem for its merits, I have a fondness for this selection because I've seen an early draft and am fascinated to see this poem as a work in progress. I look at his choices (what he keeps and what he changes) as well as the metrical aspects of the work. The imagery in the finished poem is effective and nostalgic. Consider the following line:
A child sitting under the piano, in the boom of the tingling strings
I've attached a site with both versions of "The Piano" in case you want to take a look for yourself. In order to choose the "best," I'd recommend you do some reading on your own to determine your preferences rather than relying on mine or any other editors'.