I want to allow content creators access to admin page and let them create and edit blog posts. This as far as I know is currently only possible if Lektor is running in development mode - then one can open admin end edit in CMS.
Is there any way someone can manage blog without running their own instance?
what you are asking for defies the purpose of a static site generator. Lektor explicitly generates static content so that you do not have to host a CMS. That being said, you can host the development mode on your server to allow editing. Though I am not sure what the limits are, especially on concurrent use. And you want to add an authentication layer to prevent unauthorized users from editing your website.
TLDR: no, you can not. You have to run a dev server instance.