Trying to Locate the Lynch Family in Australia

[Definos]

 I am looking for my 2nd Great Grandfather Terence Francis Lynch, originating from Ireland but arrived in Victoria, Australia in 13 Dec 1873. I have done quite a bit of research but at a standstill. It seems like a troubled life for all concerned but I am hoping to find out what happened to him after 12 Jan 1878 when the Emerald Police Station arrested him for a second time for deserting his wife Mary (Barrett).
Daughter Frances Lynch is my Great Grandmother, married and moved to NSW. Edward (Timy??) and John Joseph were in trouble with the law in Victoria. I found out that Edward died through stories in the newspapers. John Joseph is a mystery. Ernest moved to WA - he was in the Army. His son become a well-known violinist. All the details are as below.
I hope you can help me unravel what happened to Terence and Mary and John Joseph in Victoria. My sincere thanks in advance. I do not have birth or death records for Terence Francis or Mary Barrett's birth records as have not been able to locate.

Terence F Lynch Birth: Abt. 1838. Castlebar Parish, Mayo, lreland
Military: 1855 - 1873 . Joined the British Army >
First name(s) Terrance Lynch. Service number 4194 WO97 Chelsea Pensioners British army service records 1760-1913
Marriage: 22 Apr 1867. Terence Francis Lynch and Mary Barrett (1844-)Mallow, Cork Cork, Ireland
lreland Marriages 1845-1958 Transcription 1867 in Mallow, County Cork Ireland. Reg. year 1867. Reg. Qtr/Year 1867 Registration district Mallow Volume 10 Page 289
Birth of Son > Edward James Lynch (1869-1905) 15 Jan 1869. Cawnpore, Bengal, India
Birth of Son > Timothy (Timy) Lynch (1870-1906) Abt 1870. lndia (*I believe Edward and Timy might be the same person)
Birth of Son > John Joseph Lynch (1870-) 23 Jul 1870 . Calcutta, West Bengal, lndia
Birth of Daughter > Frances Lynch (1872-1945)
Calcutta, West Bengal, lndia
Arrival: 13 Dec 1873 . Melbourne, VIC, Australia. Recorded as TT Lynch plus Mrs pIus 3 children arriving on ship Ben Nevis from Calcutta
Separation: 10 Nov 1874. Emerald Hill, Victoria, Australia. Terence Francis Lynch deserted his wife Mary twice leaving her and 4 children destitute -2 children made wards of the state of Victoria in 1874 but only until 1875
Birth and Death of Son Frederick Lynch (1875-1875) 1875. Emerald Hill, Victoria, Australia
Residence 1875 > 31 Alfred 5t, Emerald Hill, Victoria, Australia
Birth of Son: Ernest Edward (Edwin) Lynch (1876-1943) 1876. Emerald Hill, Victoria, Australia
Arrested for Wife Desertion: 25 Sep 1876 . Mentone, Victoria, Australia. Arrested at Mentone Police Station
Separation: 30 Jul 1877. Emerald Hill,Victoria, Australia. Terence Francis Lynch again deserted his wife Mary.
Arrested for Wife Desertion: 12 Jan 1878. Emerald Hill,Victoria,Australia. Arrested at Emerald Hill Police Station.
Death of Son: Edward James Lynch (1869-1905) 24 Dec 1905 . Cobram, Victoria, Australia (* Same person I believe)
Death of Son: Timothy (Timy) Lynch (1870-1906) 1906. Cobram, Victoria, Australia (*Same person I believe)
Death of Son: Ernest Edward (Edwin) Lynch (1876-1943) 7 Jun 1943. MayIands, Western Australia, Australia
Death of Daughter: Frances Lynch (1872-1945) 4 Feb 1945. Summer Hill, New South Wales, Australia

[cupoflife]

Have you ruled this death out?
https://web.ballaratcemeteries.com.au/Deceasedsearch/DeceasedDetails.aspx?PersonId=146745&LocationId=22189
Name: Terrence LYNCH
Age: 83
Occupation: Inmate
Disposition: Buried
Cemetery Ballarat Cemetery New
Location: Benevolent, Section 1, Row 1, Grave 23
Date of Service: 29/08/1922

This is probably the death:
1922 #7722 Terence LYNCH
Father-James
Mother-Mary (Mcmanamny)
Place of death: BALLARAT
Age: 83

[judb]

You may already have these as you have read about Edward's death in newspapers.  However there is no mention of the name of "Edward" in these reports

Timothy LYNCH apparently died from the effects of a blow on the head at Cobram on Sunday 24 Dec 1905.
http://trove.nla.gov.au/newspaper/article/89538944

Thomas WARD charged with his manslaughter.
http://trove.nla.gov.au/newspaper/article/199419339

Inquest shows that he had a quarrel with a Thomas WARD and fell to the ground, but as he "was not in robust health" the other man was discharged.
http://trove.nla.gov.au/newspaper/article/199425028

This report of the incident states that LYNCH was also known as CORBETT
http://trove.nla.gov.au/newspaper/article/223513672

Edit to add:
This report uses the surname CORBETT
http://trove.nla.gov.au/newspaper/article/199408816

There are a couple of other reports in other regional papers - you can search TROVE.

Judith

[judb]

I think you are right about Edward and Timothy being the same person as the death record entries for both in Victorian BMDs have the same number and same other details, except the forename/s.

Victoria 1906 #1121
Edward Jas LYNCH, 36, died Cobram
Parents: Terence Fran LYNCH, Mary (Barrett)

Victoria 1906 #1121
Timy LYNCH, 36, died Cobram
Parents: Terence Fran LYNCH, Mary (Barrett)

Judith

[wivenhoe]

The two children in care would be John Joseph LYNCH  #8134 and Edward James LYNCH #8135.

Each file is cross referenced to name the other brother. Father is believed to have gone to India at 27 Nov 1874 admission....and mother has two other children..

(my interpretation......additional to the child named  ie three children,and this count referring to children in care).

Additionally, files#8134 and #8135 name Ann LYNCH born Melbourne 1 Mar 1866 to be their sister.

Ann LYNCH  #8153  and #3074 father William H FOWLER in India at 24 May 1874, mother died 23 May 1868. Files for Ann also name John and Edward as brothers.

Who is Ann LYNCH?

Do you have birth certificate for last born child in Victoria to see names of previous issue?

You should read through these asylum files to check these dates I am seeing.

[wivenhoe]

The Advocate 23 May 1868 p7
http://trove.nla.gov.au/newspaper/article/169265082?

This story would seem to relate to Ann LYNCH. I think that the references on the asylum files are
 incorrect, and Ann LYNCH has no connection.

[Definos]

I apologise, for some reason I wasn't getting the notifications for my post. 

I just wanted to thank you so much for you help with this family search and the information you found.  I am still trying to confirm whether or not Terence Francis LYNCH was the fellow in Ballarat who passed away in 1922. 
I've also found some other information on that is confusing me more. 
in 1901 there were two people a TF Lynch and a MJ Lynch who left Victoria for Capetown South Africa,  aboard the Orient.   Did see the online entry of these two but I am not sure if there would be any further information about them? 
Also found information on PROV  > 1901 about Edwards James LYNCH  >>>
Series title:   The Empire's Patriotic Fund Applications
Description:   225 - Edward James Lynch
South African Light Horse
Edward James Lynch
Date range:   1901 - 1901
Public access:   Open
Format:   Physical
Location:   North Melbourne
This Item is part of
Series number:   VPRS 16930
Consignment number:   P0001
Unit number:   2
Not sure about this as I have just noticed it today. 
So thanks again for your help.  Any more clues, directives or suggestions are welcomes!  I will remina logged in!
Kindest regards and thanks again
Karen