Lipid-correlated disease such as atherosclerosis has been an important medical research topic for decades. Many new microscopic imaging techniques such as coherent anti-Stokes Raman scattering and third-harmonic generation (THG) microscopy were verified to have the capability to target lipids in vivo. In the case of THG microscopy, biological cell membranes and lipid bodies in cells and tissues have been shown as good sources of contrast with a laser excitation wavelength around 1200 nm. We report the THG excitation spectroscopy study of two pure free fatty acids including oleic acid and linoleic acid from 1090 to 1330 nm. Different pure fatty acids presented slightly-different THG χ(3) spectra. The measured peak values of THG third-order susceptibility χ(3) in both fatty acids were surprisingly found not to match completely with the resonant absorption wavelengths around 1190 to 1210 nm, suggesting possible wavelengths selection for enhanced THG imaging of lipids while avoiding laser light absorption. Along with the recent advancement in THG imaging, this new window between 1240 to 1290 nm may offer tremendous new opportunities for sensitive label-free lipid imaging in biological tissues.