How to prevent body from scrolling with push-side menu

I am trying to properly implement a push-side menu plugin (Responsive Menu) into a wordpress theme. Based on SO @Congrim answer, I've managed to achieve a way to lock the body at scroll when push-menu is open (with all the elements including the header fixed) except the interactive links class=edge-ils edge-ils-with-scroll edge-ils-light which will still go Up at push-menu open.

I've saved this sequence into congrim.js file, I've enqueued the script into the theme in functions.php file:

function lockScroll() {
    if ($('body').hasClass('lock-scroll')) {
        $('body').removeClass('lock-scroll');
    }
    else {
        $('body').addClass('lock-scroll');
    }
}


/* I've implemented `onclick="lockScroll();"` in button element, 
 * using this sequence in the same congrim.js file:
 */    

$(document).ready(function() {
    $('#responsive-menu-pro-button').click(function() {
       lockScroll();
    }); 
});

Removing the jQuery wrap will not give any error in browser console (tested in Chrome) may be still a bad approach to wrapp the code like this in wordpress (?) In these conditions, unfortunately, overflow: hidden; doesn't apply, at push-side menu open, I can't use this class in CSS file/section:

.lock-scroll {
    overflow: hidden;
}

The code will allow me to use only

.lock-scroll {
    position: fixed;
}

The question:
Is there any possibility to force the code to implement overflow: hidden;* OR any other a workaround in order to have the interactive links class=edge-ils edge-ils-with-scroll edge-ils-light not going up at push-side menu open, to remain fixed at the position the viewer is clicked before opening the menu?

Please focus on the interactive links issue only, the rest of the scene is fine (header and the logo are in place like it should be, the background pictures are acting like it should as well).

LE: *overflow: hidden; it looks like will produce an unwanted body shifting effect at menu open/close, during the show/hide scrollbar, which is not happening in this stage.

LE2: congrim.js file has been replaced with body-lock.min.js by Outsource WordPress, please see the solution below.

Website testpage here.

LE3 Jan.2021: Taking in consideration Outsource WordPress's answer, is there any possibility to tweak the below code in order to be usable in more general way in other pages as well for example here like already is running here ?

I suppose that .edge-ils-item-link and .edge-ils-content-table are variables but I have no idea how to approach and adapt this, I've made some tests replacing these elements but with no positive results, maybe is not that simple, is more than that.

Also it will be great to be jQuery ready according to the latest version (at this point I am using jQuery migrate 1.4.1 and an old version of Wordpress in order to be functional at least on the page designed for).

$(document).ready(function() {
    var windowTop = 0;
    var menuOpen = 0;
    var offsetContainerList = 0;

    $('#responsive-menu-pro-button').click(function() {
        var offsetScrollList = $('.edge-ils-item-link:first').offset().top; 

        if ($('html').hasClass('scroll-lock')) {
            $('#responsive-menu-pro-container').one("webkitTransitionEnd otransitionend oTransitionEnd msTransitionEnd transitionend",
              function(event) {
                  if (menuOpen==0) {
                      menuOpen = 1;
                      $('html').removeClass('scroll-lock');  
                      $('.edge-ils-content-table').css('top', eval(offsetContainerList)-40+'px'); //change image container top position
                      $('html').scrollTop(windowTop); //scroll to original position
                  }
                  else {   
                      menuOpen = 0;             
                  }
            });
        }
        else {                
            windowTop = $(window).scrollTop();
            offsetContainerList = $('.edge-ils-content-table').offset().top;  
            $('html').addClass('scroll-lock');      
            $('.edge-ils-content-table').css('top', -offsetScrollList + 'px'); //change image container top position
        }      
    }); 
}); 

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