No, Li does not emit a sufficient number of X-rays so with EDS it cannot be seen. You should use the WDS or another technique (for example ICP, but the sample should be properly dissolved)
There are three elements (H,He,and Li) from the periodic table that cannot be analysed by eds because they do not have characteristic X-rays, see attached file:
You are flirting with the truth but not quite there yet.
Li does produce x-rays. H and He do not having only electrons only in the first shell. It is unfortunate that the JEOL chart does explain that. The only reason that I can see they left it off is because the analysis is not practical. I see that my Oxford chart also does not show an x-ray line for Li, but their software shows the line at 0.054 keV.
One issue is the absorption of x-rays by the detector window. When I began working with EDS, Be was commonly used as a window. It effectively absorbed everything below Na. Thin windows became available and they allowed detection down to B, then down to Be as they were made thinner. I don't think they will ever get to Li with windowed detectors.
Now, Oxford and probably others have demonstrated the detection of Li using a windowless detector. The spectrum I saw was collected from a block of Li (100% before oxidation) and it showed a peak, perhaps weakly. That would not make for practical analysis.
Another issue is the strobe peak that is often present near 0 keV. On our Oxford system, that is centered around 0.015 keV. Under the shaping time that I use, that tails over across the Li position. At the highest resolution setting, it does not. But remember that because of the window, there is no intensity to be seen.
FWIW, I have recently been trying to analyze B in glass. Even that is near impractical. With 4% B, the precision is 0.4% for a 400-second acquisition. Be and Li would be worse.