Hi Helen,
Nothing much for Jack and Hannah so far ... I haven't found birth records for either of them. The earliest Lyons births in Tasmania appears to be Sophia and William, children of Richard Lyons and Mary Davis, both born in 1811. After that there are no more recorded Lyons births until 1836.
Three children were born to a James Dwyer in NSW (but the mother's surname was not given, so maybe it's another couple):
Name: Edward Dwyer
Date: 1853
Parents: James / Hannah
State: NSW
Parish: Kiama, Roman Catholic
Ref. No: V18532528 70
Name: Joseph Dwyer
Date: 1857
Parents: James / Hannah
State: NSW
Parish: Shoalhaven
Ref. No: 11157
Name: Hannah Dwyer
Date: 1859
Parents: James / Hannah
State: NSW
Parish: Shoalhaven
Ref. No: 12542
There are deaths recorded for Edward and Hannah in NSW, in 1925 and 1940 respectively, as well as for William and James, all with parents listed as James and Hannah.
There were two possible James Dwyer's on the Certificate of Freedom list, just in case it's a possibility he was a convict:
Name, Ship, Date, CF No, Date, SRRef, Film
DWYER James, Marquis of Huntley, 1828, 34/0403, 14 Apr 1834, 4/4321, 992
DWYER James, [Alias] DWYRE, Anne & Amelia, 1825, 31/0473, 10 May 1831, 4/4305, 987
Individuals with the surname Lyons feature on the Colonial Secretary's papers:
http://www.records.nsw.gov.au/indexes/colsec/l/F34c_lo-ly-15.htm#P6503_228099If you want to save a little money on the cost of purchasing the certificate for Denis' death, consider contacting Marilyn Rowan for a transcription at:
http://www.marbract.com.au/She's very accurate and timely. I've used her services a few times with excellent results.
I'll keep on searching!
Regards, Rachel