Did the Buddha ever mentioned what is the cause for having lovers / marriage?

Romance can be understood by observing as the Buddha did:

AN1.1:2.1: “Mendicants, I do not see a single sight that occupies a man’s mind like the sight of a woman.
...
AN1.6:1.1: “Mendicants, I do not see a single sight that occupies a woman’s mind like the sight of a man.

Indeed, similar observations also hold true for transgender people. In other words, romance occupies a mind. It is a feeling that leads to craving. And the Buddha explains how craving leads to seeking gain. Romance leads to the seeking and gain of romantic partners.

DN15:9.1: So it is, Ānanda, that feeling is a cause of craving. Craving is a cause of seeking. Seeking is a cause of gaining material possessions. Gaining material possessions is a cause of assessing. Assessing is a cause of desire and lust. Desire and lust is a cause of attachment. Attachment is a cause of possessiveness. Possessiveness is a cause of stinginess. Stinginess is a cause of safeguarding.

In particular, the Buddha talks about "assessing", which can apply to "counting romantic relationships."

Notably, whether one has many, one or no romantic partners, all romantic relationships have a beginning. And anything that has a beginning has an end. So if one assesses, craves and seeks romantic relationships, those exciting beginnings are bound to be followed by wrenching ends.

DN14:3.15.7: ‘Everything that has a beginning has an end.’

In contrast, giving up assessing, giving up craving, mindful of the infinite, our hearts can be released.

SN46.54:12.9: The apex of the heart’s release by love is the beautiful, I say, for a mendicant who has not penetrated to a higher freedom.

Assessing also impedes relationships. We look for partners who meet certain arbitrary criteria--we assess them and reject others. Mindful of love, compassion, rejoicing and equanimity for one and all, our hearts open to all sentient beings. We will always feel happiest around good spiritual friends. And some spiritual friends will become closer than others. I met my wife through a stranger simply because of a warm greeting. And she became my closest spiritual friend.

Note that the above is not advice to seek a relationship In fact, the Buddha specifically warns against the unworthiness of matchmaking:

DN1:1.26.2: This includes making arrangements for giving and taking in marriage; for engagement and divorce; and for scattering rice inwards or outwards at the wedding ceremony. It also includes casting spells for good or bad luck, curses to prevent conception, bind the tongue, or lock the jaws; charms for the hands and ears; questioning a mirror, a girl, or a god as an oracle; worshiping the sun, worshiping the Great One, breathing fire, and invoking Siri, the goddess of luck.

The most important causes for lasting relationships are listed by the Buddha in AN 4.55 & AN 4.53.

Also DN 31 says:

A husband should serve his wife as the western quarter in five ways: by treating her with honor, by not looking down on her, by not being unfaithful, by relinquishing authority to her and by presenting her with adornments.

A wife served by her husband in these five ways shows compassion to him in five ways. She’s well-organized in her work. She manages the domestic help. She’s not unfaithful. She preserves his earnings. She’s deft and tireless in all her duties. A wife served by her husband in these five ways shows compassion to him in these five ways.

And that’s how the western quarter is covered, kept safe and free of peril.

You may also read the Mātugāma Samyutta, which is about women; and SN 7.63, which is about seven types of wife.

Other relevant teachings of the Buddha are listed here: The Partner (A Constitution for Living ).

Geshe Michael Roach taught that the cause for finding a companion was to give companionship. He recommended nursing homes as one place to go and offer companionship to others to create the cause for relationship. He also said that there is a text that did list "deeds" and the "consequences". I am not sure if it is words of the Buddha. Unfortunately, I don't know the name and I don't think it has been translated into English. When someone wanted to change something that was sticking them, he would go into the book and find out exactly what they needed to do.

I have used the basic ideas of cause and effect to find a spiritual partner. I was looking for someone to share my spiritual journey with me and support my practice. Knowing the general idea is to do to others what you would like to have or have done to you, I figured out a way to do this. I located a person in long term retreat and set up a monthly donation to their practice. I don't think they even knew. I then dedicated my practice to their enlightenment. My current partner and I met soon after I started this, although it was a few more years before we became a couple. I am essentially a hermit, so finding a partner really is a miracle. We've been together 5 years.

To leverage cause and effect, simply find ways to help people have relationships or encourage people to stay in relationships or improve their relationships. Be creative. Offer what you would like to receive. Get detailed about what you would like to receive, do those actions, and dedicate what you do to your goal.

I was taught about a sutra called The Teaching of the Four Practices that teaches how to purify karma. Perhaps you already know a purification practice that you can undertake to clear your obstacles. You can create new causes, but always good to get rid of old causes for not being in relationship.

The four practices (or powers) in brief are:

1. Foundation power - this is simply Buddhist refuge
2. Destruction power - recognizing what you did will come back to hurt you (if you don't have a memory of it, just realize that in some life you harmed relationships - your own or others)
3. Power of restraint - resolve never to harm relationships again
4. Power of antidote - studying and understanding emptiness and karma as well as undertaking action to undo what you did (in this case, helping people stay in relationship and/or being a nice companion)