Because the LimeSurvey code (qanda.php) puts the slider handle in as a div, jquery's support for keyboard control of the slider doesn't work. (jquery puts the handle in as an "a"). It appears that Limesurvey is putting in the handle itself (as opposed to having jquery add the handle to the dom) so that it can update the position of the callout when the value on the slider is set initially:

lime-slider.js around line 63
$('#slider-callout-'+basename).css('left', $('#slider-handle-'+basename).css('left')).text(slider_prefix + thevalue + slider_suffix);

Changing that line to something similar to the one below will allow jquery to put the handle in, thereby enabling arrow key support for the slider.

$('#slider-callout-'+basename).css('left', $('.ui-slider-handle:first').css('left')).text(slider_prefix + thevalue + slider_suffix);

qanda.php would also have to change. Removing line 4237 does the trick.