The run command is only an abbreviation for the more verbose process launch -- <args>
but it works just as with GDB and therefore should be
mentioned in the GDB to LLDB command map.
For educational purposes I've not listed it as the first option on the LLDB side so that new LLDB user can, if they want, also know what the "native" way is for LLDB.
Here's the help documentation for the run command in lldb which gives
(lldb) help run Launch the executable in the debugger. Syntax: run [<run-args>] Command Options Usage: run [<run-args>] 'run' is an abbreviation for 'process launch -c /bin/sh --'