Our Mishna on Amud Aleph discusses the case of one had two mixed intentions in the critical parts of the sacrificial offering that require Lishmah. For example, if one sprinkled the blood of a chattas offering having in mind the owner/sinner who dedicated the sacrifice, and to slaughter it for another person as well, it would still be invalidated.

On a simple level, we see that when there are mixed intentions, the invalidating intention is not canceled out by the validating one. 

The Gemara Yevamos (39b) teaches:

Abba Shaul says that one who consummates a levirate marriage with his yevama for the sake of her beauty, or for the sake of marital relations, or for the sake of another matter, e.g., he wishes to inherit her husband’s estate, it is considered as though he encountered a forbidden relation, and I am inclined to view the offspring born from such a union as a mamzer. Since the prohibition against engaging in relations with one’s brother’s wife is overridden only for the sake of fulfilling the mitzvah of consummating the levirate marriage, when one does not have the intention to fulfill that mitzvah, the baseline prohibition applies, and so any offspring from the union will be mamzerim. 

The Shevus Yaakov (III:135) rules that this prohibition only applies if that is one’s sole intent, however, a mixed intent, such as because he finds her attractive as well as to fulfill the mitzvah, is perfectly fine.

Gilyonei Shas (Yevamos 39b) questions this ruling based on our Mishna. We see from our Mishna that when there is a mixed intention, the invalidating intention is not canceled out by the validating intention. Therefore, here too, if part of his intention is not for the mitzvah, then it should invalidate the process.

Yabia Omer (VI:14:8) answers that we had seen earlier on daf 3a that something which is similar can be more disruptive than that which is alien. Thus, a chattas offering that is slaughtered with the intention of an Olah offering is rendered invalid, yet a chattas offering that is slaughtered with the intention of eating Chulin (standard profane food) remains a valid chattas. The thought of a chulin (profane non-consecrated food) offering is so alien to the chattas that it has no power to disrupt it. In regard to the mitzvah of Yibum, the additional thought of marrying the woman because she is attractive, is considered a non-similar thought, because it relates to no mitzvah, and therefore just like a mixed intention for chulin does not disrupt the proper intention for chattas, so too the thought of engaging in the Levirate marriage out of finding her attractive included with the intention for a mitzvah, is acceptable and the position of the Shevus Yaakov is defended.

This brings to mind a similar and interesting halachic discussion regarding motivations for marriage. The Gemara Kiddushin (70a) states:

“anyone who marries a woman only for the sake of money, he will have offspring who are unfit.”

Interestingly, the Iggeres Hakodesh (5, bderech harevi’i) seems to hold this ruling applies in regard to beauty instead or in addition to marrying out of money, and bases it on his reading of Derech Eretz Zutah (10:6). Although its text as well seems to be different from the Ramban’s text, and also see the Gra”s text, ibid.) However, the implication from the Gemara Yevamos (ibid) we saw above, is that such an intention is only prohibited by the Levirate marriage. Still, the Ramban could easily refute this by saying that the Gemara Yevamos was addressing a more serious violation, potentially that of Kares for Eishes Ach. On the other hand, marriage for the sake of beauty, while morally improper, is not prohibited on the same level, and not being addressed by the Gemara Yevamos.

Regardless, the actual Halacha holds that the Gemara Kiddushin is regarding the choice of marrying an inappropriate woman for money, and is not even referring to a case of marrying somebody for money alone. See shulchan Aruch (EH 2:1 and Beis Shmuel 2:2.) However, Gr”a (EH 2:6) seems to uphold the prohibition for anyone to marry out of financial motivations.

Nonetheless, regardless if this prohibition applies to lustful motivations or financial motivations, we should be able to use the argument of the Shevus Yaakov that mixed motivations are perfectly fine. Indeed, the Gr”a (ibid) rules that mixed motivations are perfectly fine. And aside from the lomdus, psychologically speaking, people are quite capable of having multiple motivations, sometimes even conflicting ones. I’m not referring to self delusional denial, but even in a genuine way, it is the nature of the human personality to have conflicting feelings and thoughts. We are made in God’s image, and we can see the same operates from a mystical perspective regarding God Himself. He can have Middas Hadin and Middas Harachamim in conflict (see Gemara Berachos 7a.)