Hey there Cai; I've been away from all of this family history stuff for almost 10 years - and had never been on RootsChat before. So, it's taken me a while to review and re-validate my Toole family tree back to John and Ann (nee Trist) Toole.
Here are a few things to add to your files to perhaps help find James' (and John's) parents.
Although John and Ann (nee Trist) Toole did have one son, named - John Lawrence (exactly the same as John's brother, James' son), he didn't die young or without family as your long ago post suggests. He was my gg Grandpa. Although I have not been able to find a birth certificate, all census data, marriage records etc agree JL was born about 1824 in Exmouth, Devon (which is where his mother, Ann Trist was from). After John (the dad) died in 1838, the 1841 census shows a 41 yo Ann and a 14 yo John living with James Toole's family in St Botolph, Without Bishopsgate. Given the location, the fact that James' age and the age of his son, John (11 years old) also living there, the age of Ann and the 2nd John Toole child in the household and the likelihood that James and the late John were brothers (and that James would support Ann and JL after John's death), I am reasonably confident that this census record is the one we are both interested in.
In the 1851 Census, my gg grandfather, John Lawrence Toole, was living with his mother Ann in Trinity, Newington, Surrey AND working as a clerk at the East/West India Co - exactly like his Uncle James.
In the 1861 Census, JL was the head of household living with his wife Charlotte Trist (nee Bailey), his first daughter and his mother Ann, in Limehouse, Stepney, Middlesex and still working as a clerk (although not stated, I believe he was still at the East?West India Company.)
In the 1871 Census, JL was the head of household living with his wife, Charlotte, 3 daughters and his 4 yo son, William John Bailey Toole (my great grandfather0, and his 71 yo mother, Ann, in Kensington, London and working as a clerk in the East/West India Co.
JL died on 2 Nov 1872 in Torquay, Newton Abbott, Devon. The death certificate indicates his cause of death was "Falling off a cliff". If my history of the East/West India Co is correct, the company lost it's royal exclusivity for trade sometime in the early 1870s and closed its doors soon thereafter - which, in all likelihood resulted in JL being without employment with a wife and 4 kids in the house. My guess is - his "fall" was no accident.
Now all the above will probably not help you (because it hasn't helped me) find out who John's (and James') father and mother were. However, given that both James and John named their sons "John Lawrence", I have to believe the middle name "Lawrence" is significant to the blood line. Although I have seen no documents indicating that JL's father, John, had or used a middle name. It's possible it too was Lawrence. So, I'm going to start searching (and perhaps hire someone) to start chasing down Lawrence (first name or middle name) Toole records.
A "confounding" fact (at least to me) is that neither "Frederick" nor "Lawrence" are typical Irish names. So, assuming that Toole's father was from Ireland, it may very well be that Frederick and Lawrence came from James' and John's mother's side - and that she was actually English through and through. Just a thought....
Cheers;
Tom