It happens whenever the widget simply exists in a sidebar in the widgets admin. The errors dump to my PHP error log. I can actually see it reported by PHP with WP_DEBUG with a fresh widget instance.
[18-Aug-2017 02:49:20 UTC] PHP Notice: Undefined index: title in /Applications/MAMP/htdocs/mysite/wp-content/plugins/list-custom-taxonomy-widget/list-custom-taxonomy-widget.php on line 217
[18-Aug-2017 02:49:20 UTC] PHP 7. lc_taxonomy->form() /Applications/MAMP/htdocs/mysite/wp-includes/class-wp-widget.php:532
[18-Aug-2017 02:49:20 UTC] PHP Notice: Undefined index: taxonomy in /Applications/MAMP/htdocs/mysite/wp-content/plugins/list-custom-taxonomy-widget/list-custom-taxonomy-widget.php on line 218
[18-Aug-2017 02:49:20 UTC] PHP 7. lc_taxonomy->form() /Applications/MAMP/htdocs/mysite/wp-includes/class-wp-widget.php:532
[18-Aug-2017 02:49:20 UTC] PHP Notice: Undefined index: orderby in /Applications/MAMP/htdocs/mysite/wp-content/plugins/list-custom-taxonomy-widget/list-custom-taxonomy-widget.php on line 219
[18-Aug-2017 02:49:20 UTC] PHP 7. lc_taxonomy->form() /Applications/MAMP/htdocs/mysite/wp-includes/class-wp-widget.php:532
[18-Aug-2017 02:49:20 UTC] PHP Notice: Undefined index: ascdsc in /Applications/MAMP/htdocs/mysite/wp-content/plugins/list-custom-taxonomy-widget/list-custom-taxonomy-widget.php on line 220
[18-Aug-2017 02:49:20 UTC] PHP 7. lc_taxonomy->form() /Applications/MAMP/htdocs/mysite/wp-includes/class-wp-widget.php:532
[18-Aug-2017 02:49:20 UTC] PHP Notice: Undefined index: exclude in /Applications/MAMP/htdocs/mysite/wp-content/plugins/list-custom-taxonomy-widget/list-custom-taxonomy-widget.php on line 221
[18-Aug-2017 02:49:20 UTC] PHP 7. lc_taxonomy->form() /Applications/MAMP/htdocs/mysite/wp-includes/class-wp-widget.php:532
[18-Aug-2017 02:49:20 UTC] PHP Notice: Undefined index: expandoptions in /Applications/MAMP/htdocs/mysite/wp-content/plugins/list-custom-taxonomy-widget/list-custom-taxonomy-widget.php on line 222
[18-Aug-2017 02:49:20 UTC] PHP 7. lc_taxonomy->form() /Applications/MAMP/htdocs/mysite/wp-includes/class-wp-widget.php:532
[18-Aug-2017 02:49:20 UTC] PHP Notice: Undefined index: childof in /Applications/MAMP/htdocs/mysite/wp-content/plugins/list-custom-taxonomy-widget/list-custom-taxonomy-widget.php on line 223
[18-Aug-2017 02:49:20 UTC] PHP 7. lc_taxonomy->form() /Applications/MAMP/htdocs/mysite/wp-includes/class-wp-widget.php:532
The following appear in the PHP error log with a fresh instance, WP_DEBUG reveals more though (more of the fields):
[18-Aug-2017 02:53:40 UTC] PHP Notice: Undefined index: taxonomy in /Applications/MAMP/htdocs/mysite/wp-content/plugins/list-custom-taxonomy-widget/list-custom-taxonomy-widget.php on line 174
[18-Aug-2017 02:53:40 UTC] PHP 9. lc_taxonomy->update() /Applications/MAMP/htdocs/mysite/wp-includes/class-wp-widget.php:456
[18-Aug-2017 02:53:40 UTC] PHP Notice: Undefined index: ascdsc in /Applications/MAMP/htdocs/mysite/wp-content/plugins/list-custom-taxonomy-widget/list-custom-taxonomy-widget.php on line 176
[18-Aug-2017 02:53:40 UTC] PHP 9. lc_taxonomy->update() /Applications/MAMP/htdocs/mysite/wp-includes/class-wp-widget.php:456
You might have to check if the index in the array has a value !empty() etc to fix it.