To answer the actual question, one way to detect if users are using Lastpass is to provide some type of login field and use jQuery or similar to see if Lastpass has inserted the "background-image" it inserts into the login fields it can autofill.

Here's an example of an email input field, all the stuff in the style tag has been added by Lastpass:

    <input type="text" class="form-control" id="inputEmail" placeholder="Email" style="cursor: pointer; background-image: url(&quot;data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAASCAYAAABSO15qAAAAAXNSR0IArs4c6QAAAPhJREFUOBHlU70KgzAQPlMhEvoQTg6OPoOjT+JWOnRqkUKHgqWP4OQbOPokTk6OTkVULNSLVc62oJmbIdzd95NcuGjX2/3YVI/Ts+t0WLE2ut5xsQ0O+90F6UxFjAI8qNcEGONia08e6MNONYwCS7EQAizLmtGUDEzTBNd1fxsYhjEBnHPQNG3KKTYV34F8ec/zwHEciOMYyrIE3/ehKAqIoggo9inGXKmFXwbyBkmSQJqmUNe15IRhCG3byphitm1/eUzDM4qR0TTNjEixGdAnSi3keS5vSk2UDKqqgizLqB4YzvassiKhGtZ/jDMtLOnHz7TE+yf8BaDZXA509yeBAAAAAElFTkSuQmCC&quot;); background-attachment: scroll; background-size: 16px 18px; background-position: 98% 50%; background-repeat: no-repeat;" autocomplete="off">

This may not be the most effective way to detect if a user is using Lastpass, but it definitely works :)