In musical compositions that include vocals, lyrics significantly contribute to artistic expression. Consequently, previous studies have introduced the concept of a recommendation system that suggests lyrics similar to a user's favorites or personalized preferences, aiding in the discovery of lyrics among millions of tracks. However, many of these systems do not fully consider human perceptions of lyric similarity, primarily due to limited research in this area. To bridge this gap, we conducted a comparative analysis of computational methods for modeling lyric similarity with human perception. Results indicated that computational models based on similarities between embeddings from pre-trained BERT-based models, the audio from which the lyrics are derived, and phonetic components are indicative of perceptual lyric similarity. This finding underscores the importance of semantic, stylistic, and phonetic similarities in human perception about lyric similarity. We anticipate that our findings will enhance the development of similarity-based lyric recommendation systems by offering pseudo-labels for neural network development and introducing objective evaluation metrics.