FFMPEG Calculate Hash After Encoding Before Writing
First, a nitpick: you don't want to compute hashes on the encoded frame data before or while writing. You're testing the fidelity of the  lossless encoding so you need to compare the decoded frame of the x264 encode with the corresponding PNG.

So, first here's how to do what you specifically asked for.

Use the tee pseudo-muxer

ffmpeg -framerate 30 -start_number 0 -i "%IMAGES_DIRECTORY%\%%03d.png" ^
-filter_complex "[0]{some filter here}[otherOut]" ^
-map 0 -c:v libx264rgb -qp 0 -pix_fmt rgb24 -f tee "%IMAGES_DIRECTORY%\lossless.avi|[f=avi]pipe:" ^
-map 0 -f framehash -hash SHA512 "%IMAGES_DIRECTORY%\original.hashes" ^
-map [otherOut] {some other encoding} someOtherFile.idc | ffmpeg -f avi -i - -f framehash -hash SHA512 %IMAGES_DIRECTORY%\decoded.hashes" 




If your end goal is to check the fidelity of the lossless encoding, use

ffmpeg -framerate 30 -start_number 0 -i "%IMAGES_DIRECTORY%\%%03d.png" ^
-filter_complex "[0]{some filter here}[otherOut]" ^
-map 0 -c:v libx264rgb -qp 0 -pix_fmt rgb24 "%IMAGES_DIRECTORY%\lossless.avi" ^
-map [otherOut] {some other encoding} someOtherFile.idc


and then

ffmpeg -framerate 30 -start_number 0 -i "%IMAGES_DIRECTORY%\%%03d.png" -i lossless.avi ^
-filter_complex "ssim" -f null -


If the result is lossless, the readout will say

SSIM R:1.000000 (inf) G:1.000000 (inf) B:1.000000 (inf) All:1.000000 (inf)