After much thought, I think I finally understand your question. I'll rephrase it just to make sure we understand.
You have a hosting provider called Lightspeed (or at least that's a shortened name) with which you have an account for a shared website. You have installed Redmine within your account. However, it's current configuration is using IP addresses for redirects and/or in e-mails, so the requests using those links are not working.
If this is a correct restatement of your issue, the solution should be to edit the config/settings.yml file in your Redmine install. You should find (at least) two fields you'll want to change: 'mail_from:' and 'host_name:'. You should change 'localhost:3000' or whatever you currently have to your site's hostname. Likewise, change the entry for 'mail_from:' to your desired e-mail address. The install directions for Redmine suggest doing this from the Admin & Settings page within Redmine, but that is via the 'localhost:3000' port and thus that is likely not feasible with a shared hosting configuration. You will need to restart Rails for this change to take effect. (You could probably just change the 'host_name' field and then do the rest from within Redmine.)
Now, if the above is _not_ a correct description of what your problem is, you will need to give more detail. What is "Lightspeed" if not a web host? Please give a URL that points to what it is. What client is making the request to Redmine that needs the Host header?
