SOURCE

function isOverflow(target){
  	let cHeight = target.clientHeight;
         let sHeight = target.scrollHeight;
         return sHeight >cHeight;
    
}

function initTip(){
    const dom=document.querySelector(".panel");
    const img=document.querySelector(".panel img");
    const imgRect=img.getBoundingClientRect();
    if(isOverflow(dom)){
        
        //dom.childNodes[0].nodeValue=`${dom.childNodes[0].nodeValue.substr(6)}...`;
        dom.style.setProperty('padding-right',`${imgRect.width}px`);
        img.style.setProperty('position','absolute');
        img.style.setProperty('top','unset');
        img.style.setProperty('bottom','0');
        img.style.setProperty('right','0');
    }
}

initTip();

<div  class="panel">
   今天天气真的123123123123213123
   <img src="http://img01.yohoboys.com/contentimg/2018/11/22/13/0187be5a52edcdc999f749b9e24c7815fb.jpg" /> 
</div>

.panel{
    position: relative;
    width: 120px;
    word-break: break-all;
    overflow: hidden;
    display: -webkit-box;
    -webkit-line-clamp: 2;
    -webkit-box-orient: vertical;  
    box-sizing: border-box; 
    outline: 1px solid lightpink;
    background-color: lightgoldenrodyellow;
   
}

.panel img{
    display:inline;
    max-width: 20px;
    position:relative;
    top: 4px;
}