I have found this question immensely interesting. I beg to differ from the earlier answers posted by respectable educators. Yes, it is a love poem, but does not deal with love for memory or love for childhood, as it appears on first reading. It is an acknowledged fact about Lawrence that he had an oedipal bondage with his mother. It is the mother's shadow that falls upon all his relationships with other women. 'Piano' is a poem with covertly oedipal feelings. As the poet listens to a lady playing a piano and about to sing him a song, the poet is suddenly transported to his childhood, where he remembers his mother playing the piano on a sunday evening in a warm room which shut the chill of a winter's night. It is not the music of the piano which his mother plays upon, but it is the mother and her warmth which are of prime focus. The adult poet/Oedipus, now having lost all possibility of a reunion with his mother/Jocasta, now fervently laments the loss of childhood, a childhood significant because it was associated with the mother and the cozy warmth of her ambience. It is indeed a deeply felt oedipal poem, and since the love was too forceful to be controlled, the poet feels that his present adult existence is" cast/Down in the flood of remembrance,I weep like a child for the past". As a binary to the mother figure is the present piano player, the woman of his adulthood, who can neither provide that love nor the warmth that the potential Oedipus received from his mother/beloved, nor can she substitute the mother, for that is impossible for an Oedipus.
This is a very interesting question to consider. I think if there is a sense of love in this lyrical poem, it is one that focuses on the love of memory and nostalgia and how it is such an important force in our lives. Let us remember the power of the mental images that are evoked in the second stanza of this poem, as the adult speaker is ushered back into the past thanks to the music that he hears in the present:
In spite of myself, the insidious mastery of song
Betrays me back, till the heart of me weeps to belong
To the old Sunday evenings at home, with winter outside
And hymns in the cosy parlour, the tinkling piano our guide.
Such emotional expressions as "weeps to belong" and the memories of "old Sunday evenings at home" and the "cosy parlour" show the way in which the narrator loves the memories of his childhood past. He is so much in love with these memories, in fact, that the final stanza declares that his manhood is "cast / Down in the flood of remembrance," and the end of the poem leaves him "weeping like a child" for the past that is now irrevocably lost. If we think of this poem in connection with love, therefore, it is definitely a blind, rosy-tinged love of the past that is present, as the speaker wallows in overwhelming nostalgia. Love is present, but it is based around our concept of memory and our childhood, and conveniently ignores the various negative aspects of such a stage.
In the poem 'Piano' the speaker recalls his childhood with a sense of nostalgic fondness. He remembers his mother smiling and singing to him, as he sits under the piano with her feet in his lap. This scene is potrayed to the readers using vivid imagery:
A child sitting under the piano, in the boom of the tingling strings
And pressing the small, poised feet of a mother who smiles as she sings.
As the poet is remembering his childhood fondly we can assume that he had a happy childhood with a loving mother. The speaker's realtionship with his mother is so strong that the memre memory of her is enough to reduce him into tears. Thus, we can assume that the speaker loved his mother a lot, and that his love was mutual. Here we get a glimpse of a pure, innocent bond of love between a child and a mother.
But there is also love in the speaker's present denoted by the young woman who is singing to him at dusk with the great passion of a romantic lover:
The singer to burst into clamour
With the great black piano appassionato
So, we can say that the speaker was loved as a child as is also loved now.