To expand on Anharat's statement, the various
mysql_*() routines have been removed in PHP 7.0, so LoGD cannot work with them and PHP 7.0. However, LoGD does also include bindings for the mysqli interface, which is supported. To switch to using those, edit the file
lib/dbwrapper.php and change the following line:
define('DBTYPE',"mysql");
to
define('DBTYPE',"mysqli_proc");
then save the file, and try running the installer again.
I expect that you will continue to run into other issues of deprecated technology, but that should enable you to get further, at least.