In my native language there is a noun phrase for 'legally-married couple'. I wonder if there is something similar in the English language. I have looked up the following phrases, but they all seemed to have slightly different meaning:
As has already been pointed out on this page, legally in legally married is usually redundant. Marriage is, however, an institution that has both legal and informal social aspects, and although they usually go together, one can imagine some scenarios in which they don't. In such cases, legally married may be a useful term for focusing on the legal aspects of the relationship and setting aside the nonlegal social ones.
Two people may present themselves as married to those around them, and be perceived as married by them, but there may be some unclarity as to the legal status of their union. In such a scenario, if one needed to clarify the matter, one would want to ask whether they are legally married, and not just whether they are married, to make it unambiguous that the question is specifically about the legal aspects of the relationship.
The phrase may also be useful in the scenarios in which two people are, for the purposes of their social life, not married, but in which, because of some technicality, they are married in the eyes of the law. For example, one can say of two people who are going through a divorce, but whose divorce hasn't yet been finalised, that they are still legally married. The qualifier legally would be be very much needed in such a context, as just saying that they are married would be misleading without such a qualification.
So, to answer the question directly, legally married is an OK phrase to use, but to understand why it is used in a particular case, one needs to be aware of what in that case makes it necessary to consider the legal aspect of the marriage apart from its other aspects. Assuming that the audience is aware of that, legally married is a better term for the OP's purposes than the alternatives proposed in the question: lawful may be taken to suggest that there is something unlawful, wrong, about not being thus married, while registered is likely to be unclear to a typical audience in an English-speaking country. (Registered may, however, be on OK term, if one is writing for an audience that is familiar with the country one is writing about, and it can be assumed that the audience will recognise it as an English rendering of the term standardly used in that country's language.)
You may choose to use the noun phrase Married Couple
Marriage is the legal union of a couple as spouses. The basic elements of a marriage are: (1) the parties' legal ability to marry each other, (2) mutual consent of the parties, and (3) a marriage contract as required by law.
