you can use nav_menu_css_class
filter
add_filter('nav_menu_css_class' , 'my_nav_special_class' , 10 , 2);
function my_nav_special_class($classes, $item){
if(your condition){ //example: you can check value of $item to decide something...
$classes[] = 'my_class';
}
return $classes;
}
Using this $item you can any condition you want.
and this will add the class to the specific li and you can style the a tag based on that like so:
.my_class a{
background-color: #FFFFFF;
}