Is it possible to submit a form even though the user is not interacting with the input box?

I have a simple form and would like to submit the form but for some reason the form fails and simply refreshes the page. I am using ajax.

<ul>
<li> 1 </li>
<li> 2 </li>
</ul>

When the user clicks on the li element - the number is then displayed in the inbox using:

$(".input1").val(e.target.innerhtml); 
$(".input1").removeAttr("readonly");

(A) But when I click submit the form does not submit.

(B) However, if I manually click on the input box and insert the number 2. The form submits just fine.

I created a web app and i do not want the keyboard to appear. Instead I use css to display a scrolling list of numbers for the user to click/select from.