POSIX solution, basic:
find Father/ -type f -name lang.log -exec sh -c 'true > "$1"' sh {} \;
… -exec true > {} \; wouldn't work, the inner shell is needed because of redirection. Note the shell part is not sh -c 'true > {}', this version would be flawed.
POSIX solution, it should be faster thanks to spawning less sh processes if there are many matching files:
find Father/ -type f -name lang.log -exec sh -c 'for f; do true > "$f"; done' sh {} +
If you have truncate that can take many operands (note truncate is not required by POSIX):
find Father/ -type f -name lang.log -exec truncate -s 0 -- {} +
-- is excessive here because in this particular case every path that comes from find must start with Father/, there's no risk any of them disguises as an option. In general however, using -- before operands generated on the fly is good practice.