LibreOffice can connect directly to mail service (i.e. act as mail client software) only for mass mailing through Writer mailmerge. Setup explained by BillPodmore, but this is not what you need.
For sending current document as mail attachment, LibreOffice relies on the default installed mail client. As far as I know, you cannot use webmail for this. You have to connect an installed mail client to your mail service, and register that client software as the default mail handler. Proper mail client software is not a component of LibreOffice, but is a basic component of most user systems (Apple’s Mail.app in your case).
This does not stop you from using webmail (or other mail client software) as your go-to solution. With an IMAP connection everything is on the server anyway, so you will most likely see the same lists in inbox, sent, etc. with the same unread/read/flag/important status indicator for each message, regardless of which client/front-end you are using at the time.