Your reply.
The Latin is in the link provided by Monsignor Pope. I don’t know what the LM hymn melody means, but I’m sure your choir director dos understand that terminology.
Never heard of or used the term; LM hymn melody. I belong to a rural parish which relys on volunteers to play organ or piano for mass and other services. They rely on the new missalette issued by the diocese for the liturgical readings and the hymns to be selected listed in it. Hymns are to be congregationally sung on Sundays or the few feastdays we used to call holy days of obligation. Some hymns beside the lyrics may also include the music.
Most of hymns in it considered traditional which are very few have had the lyrics modified I suspect for copyright reasons.It also contains dozens of popular Baptist,and other Protestant denomination melodys conforming to the ecumenic direction Novus Ordo has taken. That missalette they are using might have two or three of the very traditional Catholic latin rite hymns in it. But that is it.
Example:
O SAluTARis HOStiA
Qui CAEli PANdis OSTiUM,
BelLA preMUNT hosTIliA;
Da ROBur, FER auxIliUM.