A simple (and very basic) javascript snippet to auto refresh, forcing a new file fetch (ignoring browser cache) for lovelace card images. Put this file into config/www folder and load in into your dashboard using frontend: extra_module_url setting in the main configuration.yml file

lovelace-card-image-updater.js

(function(){
    function getShadowRoots(wrap) {
        if (!wrap) return [];
        
        var found = [];
        var els = wrap.querySelectorAll('*');
        for (var i=0; i < els.length; i++) {
            if (els[i].shadowRoot) found.push(els[i].shadowRoot);
        }
        return found;
    }
    
    function findImagesInWrap(wrap) {
        var roots = getShadowRoots(wrap);
        
        var imgs = [];
        for (var i=0; i < roots.length; i++) {
            imgs.push(...roots[i].querySelectorAll('img'));
            imgs.push(...findImagesInWrap(roots[i]));
        }
        
        return imgs;
    }
    
    function updater() {
        var root = document.querySelector('body > home-assistant').shadowRoot.querySelector('*').shadowRoot.querySelector('app-drawer-layout partial-panel-resolver ha-panel-lovelace').shadowRoot.querySelector('hui-root').shadowRoot.querySelector('#layout hui-masonry-view').shadowRoot;
        //console.log("ROOT ",root);
        if (!root) return;
        
        var imgs = findImagesInWrap(root);
        
        // console.log("Imgs found: ",imgs);
        
        var k = 'lciu_random=';
        var random = new Date().getTime();
        for (var i=0; i < imgs.length; i++) {
            var newSrc = "";
            if (imgs[i].src.indexOf('/local')) {
                if (imgs[i].src.indexOf(k) !== -1) {
                    newSrc = imgs[i].src.replace(k, k+random);
                } else {
                    var sep = '?';
                    if (imgs[i].src.indexOf("?") !== -1) {
                        sep = '&';
                    }
                    newSrc = imgs[i].src + sep + k+random;
                }
                
            }
            
            if (newSrc !== "") {
                imgs[i].setAttribute("src", newSrc);
                // console.log("Updated image ",imgs[i].src, newSrc);
            }    
        
        }
    }
    
    // twice per minute
    window.ich = setInterval(updater, 1000 * 30);
})();