Styling Taxonomy Terms Individually

You could use the slug of each term as class name (and do the styling via CSS)

<?php

echo '<div class="col-lg-3 ' . $term->slug . '">'; // $term->slug is the class name
echo '<a href="' . esc_url( $term_link ) . '">' . $term->name . '</a>';
echo '</div>';

?>

If you want to use dynamic terms and colors I recommend the Mark Posts Plugin; it is possible to manage the terms/colors in the admin area and you can also display the terms/colors in the front end as you can see here:

<?php

/*
 * Display terms & colors of a post
 */

$post_markers = wp_get_post_terms( $post->ID, 'marker' );

echo '<ul>';

foreach ( $post_markers as $post_marker ) :
  echo '<li>';
  echo __('Marker', 'textdomain') . ': ' . $post_marker->name  . '<br />';
  echo __('Color', 'textdomain') . ': ' . $post_marker->description . '<br />';
  echo '</li>';
endforeach;

echo '</ul>';

?>