Miss Kilman is presented as a character who harbours feelings for Elizabeth that are so strong she feels overpowered by them. She is well aware that she loves Elizabeth with a love that is passionate and excessive, and that the more she shows that love, the greater the risk that she will drive Elizabeth away. Note how this love is described in the novel:

She was about to split asunder, she felt. The agony was so terrific. If she could grasp her, if she could clasp her, if she could make her hers absolutely and forever and then die; that was all she wanted. But to sit here, unable to think of anything to say; to see Elizabeth turning against her; to be felt repulsive even by her--it was too much; she could not stand it. The thick fingers curled inwards.

Although the novel never openly states that Miss Kilman is a lesbian, it is clear from this quote that she definitely feels a romantic and passionate love towards her. Note Miss Kilman's desire to "grasp her... clasp her... maker her hers absolutely and forever and then die..." which clearly suggest that her feelings towards Elizabeth go beyond those of a close friend. The tragedy of Miss Kilman's position is that the more she seeks to express her love the more that Elizabeth will be driven away. Her feelings towards Elizabeth are therefore the evidence that suggests she can be considered a lesbian.