Apache rewrite rule for normalizing case - .htaccess

Question

I run a web-accessible linguistic database on a server. The file lexirumah in the document root of my server contains a WSGI python script serving the application.
I want the application to be available on all matches, independent of case, of http://www\.example\.eu/lexirumah?/?. Currently, I am using the following .htaccess file.
RewriteEngine On
RewriteCond %{HTTP_HOST} !^www.example.eu$ [NC]
RewriteRule ^(.*)$ http://www.example.eu/$1 [L,R=301,NC]
RewriteRule ^lexirumah?$ http://www.example.eu/lexirumah/ [L,R=301,NC]
RewriteRule ^lexiruma/$ http://www.example.eu/lexirumah/ [L,R=301,NC]
RewriteRule ^LexiRumah/$ http://www.example.eu/lexirumah/ [L,R=301]
Options +ExecCGI
<Files "lexirumah">
SetHandler fcgid-script
</Files>
When I change the last RewriteRule to
RewriteRule ^LexiRumah/$ http://www.example.eu/lexirumah/ [L,R=301,NC]
I get an infinitite number of redirects. I want to keep the 301 status for the non-canonical URLs, so I tried
RewriteRule ^lexirumah/$ http://www.example.eu/lexirumah/ [L]
RewriteRule ^lexirumah?$ http://www.example.eu/lexirumah/ [L,R=301,NC]
RewriteRule ^lexiruma/$ http://www.example.eu/lexirumah/ [L,R=301,NC]
RewriteRule ^LexiRumah/$ http://www.example.eu/lexirumah/ [L,R=301,NC]
leading to an internal server error. (Presumably the infinite redirection loop that was caught by my browser previously now happens inside mod_rewrite?)
Now I have changed the rules to use a RewriteCond to skip the case normalization when it is already lowercase.
RewriteCond %{REQUEST_URI} !^/lexirumah/$
RewriteRule ^LexiRumah/$ http://www.example.eu/lexirumah/ [L,R=301,NC]
RewriteRule ^lexirumah?$ http://www.example.eu/lexirumah/ [L,R=301,NC]
RewriteRule ^lexiruma/$ http://www.example.eu/lexirumah/ [L,R=301,NC]
Does this set of rules do what I want it to do, or are there any hidden pitfalls that I need to take into account?

Answer 1

Short answer
Yes, your set of rules does what you expect.
Note, though, that you could simply use ^lexirulah/$ in first RewriteRule, since you include the NC flag. As a consequence, the matching will be case-insensitive (No Case). Official documentation of NC flag can be found here.
Also, you don't need a full url (host included) to redirect. You can directly use RewriteRule ^xxxx$ /lexirumah/ [L,R=301,NC] for each rule.
Your initial question
When I change the last RewriteRule to
RewriteRule ^LexiRumah/$ http://www.example.eu/lexirumah/ [L,R=301,NC]
I get an infinitite number of redirects.
If you think about it, it's easy to understand why you end up with an infinite loop. Since NC matches in case-insensitive mode, your redirect will always match your rule, again and again.