In the spirit of Rootschat cooperation, I have downloaded the RN record.
It does not unfortunately give any family details BUT there are some helpful clues. First it gives his date of birth as 13 July 1882, the National Archives have transcribed this wrongly in the catalogue. Secondly it gives his "home port" as Devonport which would chime with births in the Devonport district. It gives what looks like a home address in St Dominick Cornwall (near to Devonport) in 1919 when he finished his Great war service.
There is an address at 12 Furneaux Avenue Plymouth in 1939 just before his second war service. The property is given as vacant on the 39 Register but Beatrice R Leach born 23 Apr 1883 is on the register at another Plymouth address. There is one other name but that record is closed.
He served from 1939 until 1946, serving in Scotland and later Devonport again. This is the man in the Navy lists already cited.
Regarding his rank. There are two possibilities. Either, as is quite normal, his substantive rank, the one that is quoted in official records was Lieutenant and he had been promoted in a temporary or acting capacity to the next rank up (Lieutenant Commander) although there is nothing about that on his record. Or, as again happens often, the family is mistaken in recalling his rank as Lt Comd.
There is only one Navy List which is the official Navy publication of all officers serving and retired in the period of publication and there is only one Edward Leach in the relevant time frames. The same man also appears in the RN medal list for the Great War.
In 1911, Edward Leach, in the Royal Navy, age 29, with wife Beatrice Rosina and children Edward Robert George and Beatrice May and sister in law Alma Pridham are living in Devonport.
I am in no doubt that this is the man we are looking for.
maxD