Think you've found your issue. Have never heard of, nor have I ever run, a moodle of higher version (basically) 'inside' a moodle of an older version. Have run them side by side and still do that on some servers.
Here's why it's a problem ... many changes/exceptions to apache can be done via .htaccess files ... but .htaccess files are heirarchial ... the one at the highest folder level rules the roost for all below it.
To avoid clash ... one might need to run virtual apaches ... which means different FQDN's ... the moodle at: /xxx/moodle is accesed via https://somenet.net whiie the moodle (which is now in lms and needs to be moved) up one level ... is accessed by https://lms.somenet.net/
Now one could run just one FQDN but the two moodles would have to be in subdirectories (no conflicts then) ... this way, server is accessed via https://somenet.net ... to access the original moodle https://somenet.net/moodle/ to access the newly migrated would be https://somenet.net/lms/
Since this is CentOS 7.1, am curios as to why one is not using defaults for apache on that OS ... which places document root at /var/www/html/ ... that would be perfect for location of the old 'moodle' directory as well as a directory for the new 'lms' (side by side).
Default config of apache on 7.1 also knows about /var/www/ ... which for all practical purposes is 'apache' users/group 'home' directory and a logical location for the data directory for the original moodle ... /var/www/moodledata/ *and* for the data directory for the new moodle's data /var/www/lmsdata/
So you have, I think, some moving to do ... and after the moving ... changes to config.php files as well as search and replace tool in both instances to change the URL's to the instances.
You can, however, continue to fit a square poll into a round hole if you wish ... but think it would break too easily and be rather difficult to admin ... no directions/tutorials, etc found about Moodle found anywhere on internet would apply.
Now if all this started this way, could be you were reading docs on how setup a moodle on Ubuntu of old and should have found/been following docs on a Linux Standards Based OS ... Ubuntu 16.04 or CentOS 7.1. Which is kinda a warning about docs ... make sure you find the docs that pertain to CentOS 7 and if you can not find one and are reading Ubuntu 16.04 be sure to translate Ubuntu-ese to CentOS-ese - similar, but do have diffs.
'spirit of sharing', Ken