The ancients called the third lunar month 'late spring.'
Tips
culture
Each season is split into 孟 (mèng, first month) → 仲 (zhòng, middle month) → 季 (jì, last month). So 孟春/仲春/季春 are the three lunar months of spring; 季夏 / 季秋 / 季冬 follow the same pattern. 季春 = 农历三月.
memory
Don't confuse 季 here ('last in a series') with 季 meaning 'season' (一年四季). Both meanings sit in the same character — the 'youngest sibling' sense (季子) gives rise to 'last/youngest of a sequence'.