for lh in lh*; do
cat "$lh" "rh${lh#lh}" >"merge${lh#lh}"
done
This will concatenate each `lh` file with the corresponding `rh` file and save the concatenated version as `merge` (followed by whatever comes after `lh` in the filename).
The parameter expansion `${lh#lh}` will remove the string `lh` from the start of the value of `$lh` (e.g. turn `lh.BA.stats` into `.BA.stats`).