When Lake gave her clues, the very first group I thought of was Phi Mu.
I have a funny way of thinking about things an I tend to zone in on random details. (As you all have probably noticed from my previous AI guesses!! LOL). Lake said:
"It's sort of ironic that I found out I'll be able to pledge my lifelong loyalty to this house on or around St. Patrick's Day"
Phi Mu's symbol/badge is a quatrefoil.
A quatrefoil, as defined by Merriam Webster -- 1 : a conventionalized representation of a flower with four petals or of a leaf with four leaflets. 2 : a 4-lobed foliation in architecture
St. Patrick's Day.....four-leaf clover ..... quatrefoil....."4-lobed foliage" ......
That's my guess and I'm stickin' to it!
.....Kelly