So after a lot of digging around I'm pretty sure there isn't a shortcut to do this, or even a specific command that can be mapped to a shortcut. Rather one must find the action from a list. So I had to write a function to automate that as follows:
;; Inline variable
(defun lsp-rust-inline-action ()
"Execute the Rust Analyzer inline refactor code action."
(interactive)
(lsp-request-async
"textDocument/codeAction"
(lsp--text-document-code-action-params)
(lambda (actions)
(let ((inline-action
(seq-find (lambda (action)
(string= (gethash "kind" action) "refactor.inline"))
actions)))
(if inline-action
(lsp-execute-code-action inline-action)
(message "No inline action available here"))))
:error-handler #'lsp--error
:mode 'detached))
(with-eval-after-load 'rust-mode
(define-key rust-mode-map (kbd "M-v") #'lsp-rust-inline-action))
So after adding this to my ~/.emacs.d/init.el I can inline variables with M-v (ALT + v).
NOTE: It doesn't seem inlining is always available for all variables, it seems the rust-analyzer only supports a subclass of situations - this can make things very confusing.
inline_local_variable