According to NSW State Records, they came as 'unassisted arrivals', i.e they paid their own way.
In 1847, he married Ann McCulloch at St James Church of England, Sydney.
In September 1847 he was running a Livery Commission Stables in Pitt Street, Sydney near today's Park Street and the Sydney Town Hall.
The Sydney Morning Herald, Tuesday 7 September 1847
LIVERY COMMISSION STABLES, PITT-STREET, SYDNEY, OPPOSITE THE SCHOOL OF ARTS.
LAWRENCE MAWBY, late of Darlinghurst, begs most respectfully to inform his friends, the public, and gentlemen visiting Sydney that he has taken those capacious and convenient premises lately occupied by Mr. Mark Dixon, as Livery Stables, and opened the same as Livery and Bait Stables, upon the same principal as "Elmore's, of the Edgeware Road, London," and in soliciting the patronage of gentlemen, he begs to assure them that the most guarded and careful attention will be paid to all horses standing at livery as well as bait. The terms will be found to be most reasonable upon trial.
N.B.-Saddle horses ; gigs, to be let on hire ; horses broken in, to single and double harness, &c, &c. 3852 [Source:http://nla.gov.au/nla.news-article12900310]
The Sydney Morning Herald, Thursday 6 January 1848
FOR SALE; a handsome light Carriage, adapted for one or two horses ; also, a set of splendid double Harness, all nearly new. It will be sold quite a bargain, the present owner having no further use for it. Apply to Mawby 's Livery Stables. Pitt street. 316 [Source:http://nla.gov.au/nla.news-article12895203]
On 19 February 1848, he was sequestered for insolvency.
At that time he was living in Pitt Street and was a horse dealer.
He and his wife then moved to Queensland [via New Zealand and England].
[For more about the Queensland Mawbys, click on the Mawbey Family Australia-Queensland link in the sidebar of this blog.]