I was intrigued by your question so I had to read this myself. Actually both guys loved each other. The way I see it, this is what this oneshot meant:
The soldier, José was Lucas' lover. However, given the fact that Lucas is a celebrity and a lady killer, José had doubts about his feelings (hence, he asked him whether he loved him but then told him not to answer this question. If he were sure that the other guy loved him then he wouldn't have refused to hear the answer).
As the story unfolds we realize that Lucas did love José (the soldier) but was jealous of Carmen. His jealousy was triggered by the words José used to describe her: a woman who catches the eyes of every man who sees her. In addition to that José kept the flower he received from Carmen. Lucas concluded that José had fallen under the spell of Carmen, hence he reacted by seducing her and making sure that José saw them. In reality, Lucas had no interest in Carmen but she was his rival and by snatching her away, he wanted to make sure that she won't be a threat anymore. He was "protecting" his pretty lover who would make any gypsy girl turn green with envy (this means that he saw José as someone who is even prettier than Carmen).
As the story progressed, we realize that Lucas was a possessive and jealous lover who wanted Carmen to be eliminated.
In the story, Lucas would give the bull to the woman he was officially going out with. Hence, he presented the first bull to the duchess, whom he was going out with at the time, and he should have presented his next bull to Carmen but José asked him not to do that. Receiving the bull from Lucas was symbolic for José as it meant, at least in his eyes, that he was acknowledging him as his lover. However, Lucas, acting upon his sinister and dark jealousy, requested an offering in return of presenting the bull to José. Blood in exchange of blood, Carmen's blood in exchange of the bull's blood.
The ironic part is that both of them never confessed about being in love with each other. Lucas never told José that he loved him, albeit he did, and José never "explained" that he was infatuated with Carmen not because he loved her but because he wanted to be like her; why, you ask? Because he was insecure, if he were a woman then Lucas could openly go out with him. If he were as pretty as Carmen, he thought, he would be able to compete with other women and supersede them. José's infatuation with Carmen only meant that he wanted to be loved in the open, not in the dark, which was impossible at the time, because both of them are men.
You're welcome (●￣(ｴ)￣●)