Q: can a person with no legal standing contact and hire the probate lawyer?

A: Probate matters can include guardianships, conservatorships, adoptions, and involuntary commitments, so the answer to who might be eligible to initiate or involved in a probate proceeding could have lots of different answers. Limiting the answer to probate matters involving decedent's estates:

Reading your question literally, yes, a person with no legal standing contract and hire a probate attorney, the answer is yes. Your question is probably "Who has standing to initiate a decedent's estate?" Persons who traditionally are considered to have standing to participate in a probate case are heirs at law (who would receive the estate if there is no will); legatees and devisees (who might be listed in the will to receive personal property or real estate, respectively); executors, persons in possession of the original will, and creditors of the estate. If an heir, legatee, or devisee is a minor or mental capacity, a case may be filed on their behalf by a "next friend" adult. Likewise, a conservator of any pecuniary interest in the estate could file a case. A party that holds an asset of the estate would probably be considered an interested party (e.g, a farm tenant has a check for the harvested crop). It would not be unimaginable that a friend of a non-heir member of the family might initiate a case and a court would proceed on the estate for the benefit of creditors, heirs at law, legatees or devisees. So, the possible universe of possible initiators is pretty broad. As for who has an interest in the estate, the creditors, heirs at law, legatees and devisees (and their possible representatives) are the people whose interests shape how the case will proceed, with some role for the named executor of the estate.