Sorting entries A-Z, ignoring 'The' and grouping by first letter
That SQL code snippet Brad posted only works with the order parameter.
The group filter doesn't allow SQL, but you could try to replicate the logic using Twig's ternary operator.

{% set artists = craft.entries.section('lineup').order('(CASE WHEN field_sortTitle IS NULL OR field_sortTitle = "" THEN title ELSE field_sortTitle END)') %}
{% set artistsGrouped = artists|group('{ object.sortTitle ? object.sortTitle[:1]|upper : object.title[:1]|upper }') %}

{% for letter, artistsInGroup in artistsGrouped %}
    {{ letter }}
    {% for artist in artistsInGroup %}
        {{ artist.title }}
    {% endfor %}
{% endfor %}


To shorten the expression a bit I used the slice filter's short syntax [:1] instead of |slice(0, 1).