To receive a copy of all the emails you send using LSP.expert, you simply have to select the corresponding option under Settings > Profile.
If you integrated your LSP.expert account with your SMTP server, you won't get a copy of the emails you send, but you will find your sent items in the Sent folder of your mailbox. To know how to integrate your LSP.expert account with your SMTP server, see this article: https://help.lsp.expert/en/articles/2747074-can-i-link-my-lsp-expert-account-to-my-smtp-server.