Interesting problem Ron and Anouk,
I assume making the changes across the entire site is acceptable. There are over 500 strings in the../mod/lesson/lang/en file. You can modify these under site administration via lesson.php. I do not recommend going into ../mod/lesson/lang/en/lesson.php file and editing it. Let moodle make a second file as part of your moodledata files with just the strings you changed.
You might want to change the
congratulations' string = 'Congratulations - end of lesson reached';
displayscorewithoutessays string = 'Your score is {$a->score} (out of {$a->grade}).';
yourcurrentgradeisoutof string = 'Your current grade is {$a->grade} out of {$a->total}';
There are also strings to display when there are essay questions. You might find some other interesting strings you might change in that file.
I would either put in new text or something like a "-" in my edits.
A more tedious interface approach is via HTML/css code. I think I agree with Ron about the classes. At first glance, I do not see unique classes that scream "Lesson" at me. They seem like they are generic to all of Moodle and are inserted via something like a view.php script. Perhaps my HTML/css skills, like my PHP code skills are very limited.
Enjoy!
Chris