Dictionary creators who are not trained in linguistics or lexicography are in good company.
Samuel Johnson (1709-1784) created his A Dictionary of the English Language between the years 1746 and 1755 (year of publication). Johnson was not trained in linguistics or lexicography; he never finished university because he ran out of money.
Johnson used hundreds of books (his "corpus") as sources for quotations or example sentences. His dictionary contained approximately 114,000 literary quotations (Shakespeare, Milton, Dryden, etc.). Johnson's dictionary remained the most influential English dictionary until the completion of the Oxford English Dictionary or OED in 1928 (the first volume of the OED was published in 1888). In addition, as Michael Adams wrote, Johnson made dictionaries matter.
The original authors of the Deutsches Wörterbuch, Jacob Grimm (1785-1863) and his younger brother Wilhelm Grimm (1786-1859) both studied law, not linguistics or lexicography, at the University of Marburg. Their dictionary also uses quotations. The Deutsches Wörterbuch is to the German language what the OED is to the English language.
The above are monolingual dictionaries, so I have only proven that unprofessional monolingual dictionaries have been produced in the past.
I should also give at least one example of a bilingual dictionary.
The Italian Giovanni Florio (1553-1625, better known as John Florio) was a language tutor at the court of James I of England but was not trained as a linguist or a lexicographer. In 1598 he published an Italian-English dictionary entitled A World of Words, which he expanded and republished in 1611 under the title Queen Anna's New World of Words, or Dictionarie of the Italian and English tongues, Collected, and newly much augmented by Iohn Florio, Reader of the Italian vnto the Soueraigne Maiestie of Anna, Crowned Queene of England, Scotland, France and Ireland, &c. And one of the Gentlemen of hir Royall Priuie Chamber. Whereunto are added certaine necessarie rules and short obseruations for the Italian tongue. The dictionary uses quotations, though not for all entries. (It is not clear what Florio's corpus would have been.) Both versions of the dictionary can be downloaded Greg Lindahl's website, who also provided a searchable version.
Ambrogio Calepino (c. 1440–1510) wrote a Latin dictionary that was first published in 1502. It cited classical sources. Later, in the 1580s, Jesuits in Japan used it as a basis for the Dictionarium Latino Lusitanicum, ac Iaponicum (DLLI), a Latin-Portuguese-Japanese dictionary, which retained only part of the quotes from classical authors. See Emi Kishimoto: Annotations in Dictionarium Latino Lusitanicum, ac Iaponicum (1595) in the Context of Latin Education by the Jesuits in Japan (PDF).