"I make a great difference between people. I choose my friends for their good looks, my acquaintances for their good characters, and my enemies for their good intellects. A man cannot be too careful in the choice of his enemies. I have not got one who is a fool. They are all men of some intellectual power, and consequently they all appreciate me. Is that very vain of me? I think it is rather vain." (1.18)
Lord Henry's view on other people is basically summed up here: he's only interested in what other people can contribute to his life, not to building real relationships.
Lord Henry Wotton
"You are glad you have met me, Mr. Gray," said Lord Henry, looking at him.
"Yes, I am glad now. I wonder shall I always be glad?"
"Always! That is a dreadful word. It makes me shudder when I hear it. Women are so fond of using it. They spoil every romance by trying to make it last for ever. It is a meaningless word, too. The only difference between a caprice and a lifelong passion is that the caprice lasts a little longer."
As they entered the studio, Dorian Gray put his hand upon Lord Henry's arm. "In that case, let our friendship be a caprice," he murmured, flushing at his own boldness, then stepped up on the platform and resumed his pose. (2.19-20)
Friendship, to Lord Henry, is certainly not a matter of loyalty – it's a matter of enjoyment, and living for the moment. This is fairly representative of his whole approach to life, not just relationships.
He had known Basil Hallward for months, but the friendship between them had never altered him. Suddenly there had come some one across his life who seemed to have disclosed to him life's mystery. And, yet, what was there to be afraid of? He was not a schoolboy or a girl. It was absurd to be frightened. (2.16)
Dorian's understanding of friendship is starting to change. He wonders what this strange new acquaintance (Lord Henry) will do to him, and he already starts to feel himself on the brink of some transformation.
Lord Henry Wotton
Talking to him was like playing upon an exquisite violin. He answered to every touch and thrill of the bow. . . . There was something terribly enthralling in the exercise of influence. No other activity was like it. To project one's soul into some gracious form, and let it tarry there for a moment; to hear one's own intellectual views echoed back to one with all the added music of passion and youth; to convey one's temperament into another as though it were a subtle fluid or a strange perfume: there was a real joy in that -- perhaps the most satisfying joy left to us in an age so limited and vulgar as our own, an age grossly carnal in its pleasures, and grossly common in its aims... (3.5)
The blossoming "friendship" between Lord Henry and Dorian seems to be nothing but a self-indulgent exercise for the former, who really seems to love hearing the sound of his own voice – or at least, of his own ideas.
Dorian Gray drew a long breath. The colour came back to his cheeks, and a smile played about his lips. The peril was over. He was safe for the time. Yet he could not help feeling infinite pity for the painter who had just made this strange confession to him, and wondered if he himself would ever be so dominated by the personality of a friend. Lord Henry had the charm of being very dangerous. But that was all. He was too clever and too cynical to be really fond of. Would there ever be some one who would fill him with a strange idolatry? Was that one of the things that life had in store? (9.12)
Dorian is intrigued and contemptuous towards Basil's confession of his adoration – he himself is never moved that strongly by people, and we also have to wonder if he's lost the capability to truly connect to others…or if he ever had it at all.
How much that strange confession explained to him! The painter's absurd fits of jealousy, his wild devotion, his extravagant panegyrics, his curious reticences -- he understood them all now, and he felt sorry. There seemed to him to be something tragic in a friendship so coloured by romance. (9.14)
We have to feel for poor Basil here – it's obvious that his passionate love/friendship will always go unreciprocated by Dorian. While the younger man does feel fond of the painter, he certainly doesn't feel anything approaching the same degree of idolatry; what's implicitly tragic about this friendship is that it can't ever blossom into actual "romance."