Get the size of the file:
$ wc -c myfile.jsons 104431233268 myfile.jsons
Then pipe it through
head to take only e.g. 1/1000th of the file:
cat myfile.jsons | head -c 104431233 | wc -l 213657
Our file should then have
213657*1000 = 213,657,000 lines.
Of course, it only works if the length of your lines is uniform.