The definition of petrin as ‘religious house’ stems from the phrase domos ecclesiasticos used in the corresponding Latin source text. An alternative rendering of the same Latin source as maisuns confirms this (‘De l’iglise de saint Lorenz Toli treis maisuns le dolenz’ Adgar3 91.17-18). The editor of Mir N-D consequently interprets the word as a corrupt variant of prestrin (otherwise not attested in medieval French, cf. Gdf 6,395c) – an adjectival form of prestre meaning ‘of a priest’, here used as a noun to refer to a religious house. This theory is reflected in AND1 and the DEAF (but nowhere else), and is retained here in the second edition, albeit with a strong caveat: such an interpretation presupposes an aberrant spelling of a rare word used earlier than expected in a different grammatical category with an otherwise not attested sense, purely on the basis of context and parallel passages.
It may be necessary to investigate other perhaps more plausible interpretations. The word is used in rhyme with engin, and may have been selected by the Anglo-Norman author purely for that reason. Two lines later the church of St Anne is referred to somewhat obliquely as un [...] purpris, i.e. ‘a precinct’, again for reasons of rhyme. As such, the word petrin may be understood as a variant spelling of the well attested pestrine1, i.e. 'bakehouse', serving as a somewhat awkward pars pro toto for a monastery. Alternatively, it may be that the word is a vernacular representation of the Latin adjective petrinus (DMLBS 2258b), ‘made or consisting of stone’, used substantively to refer to a stone building. However, such a use is not attested elsewhere (in Latin or French).