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The Golden Eagles had a 242, while Shenandoah finished with 213 and Rushville carded a 218.
Sidney Steele led Lincoln with a 57.
The other scores for the Golden Eagles were Alex Cox (61), Lydia Bertsch (62), Makala Hammons (62) and Mallory Kern (63).
Lincoln returns to action on Thursday with a tri-match with Blue River at Daleville.