Another lane swerve, since I'm not a Beta.
I believe it was once very common to wear badges on lapels; I've seen lots of old (as in early 20th Century) pictures from various fraternities where badges are on lapels. Over time, that practice seems to have faded in favor of wearing the badge directly over the heart. In some fraternities this is by rule (our General Regulations forbid wearing our badge on a lapel) while in others it may be by custom.
FWIW, Chapter XV, Section 2, of Beta's Code (which is
online) says that the badge is "to be worn over the heart and in a manner befitting the honor and dignity to which the badge is entitled." A Beta would have to say whether wearing the badge on the lapel satisfies this provision.