The present study was conducted to determine the critical optimum and toxic concentrations of potassium (K) using segmented analysis and its relationship with some physiological, anatomical, and nutritional responses to increasing K in hydroponically grown Lilium sp. L. cv. Arcachon. Plants were fertigated with nutrient solutions containing K (Kext) at 0, 2.5, 5.0, 7.5, 12.5, 17.5, 22.5, and 30 mmol·L−1. Maximum flower diameter occurred when, on a dry mass basis, shoot K (Kint) ranged from 504 to 892 mmol·kg−1; however, a lower Kint was required to obtain maximum biomass accumulation and shoot length (384 and 303 mmol·kg−1, respectively). Potassium increased in all plant organs as K in the nutrient solution increased. Nitrogen increased in young leaves and magnesium (Mg) decreased as Kext increased. Concentrations of Kext from 5 to 17.5 mmol·L−1 increased the size of chlorenchyma and occlusive cells; however, metaxylem vessels were unaffected. Net photosynthetic rate was higher in young leaves, whereas water potential increased in both young and mature leaves when Kext was greater than 22.5 mmol·L−1. Critical concentrations varied according to the growth parameter. Optimum Kint ranged from 303 to 384 mmol·kg−1 for vegetative parts, whereas parameters related with flower growth ranged from 427 to 504 mmol·kg−1. Concentration of 504 mmol·kg−1 Kint was associated with optimum growth for all the parameters assessed, whereas a Kint greater than 864 mmol·kg−1 was associated with a decline in growth; thus, these concentrations were considered as the critical optimum and critical toxicity levels, respectively. The optimum and toxicity critical Kint were estimated when Kext in the nutrient solutions was 5.6 and 13.6 mmol·L−1, respectively.