IGI has an entry showing the marriage as 6 Dec 1824 at St Matthew's WINDSOR - however it's a submitted entry so needs to be treated with caution.
NSW BMDs index shows the marriage:
1824 Reg # V18243462 3B
Miles LAKE
Jane ARTHUR CC (CC is the church code for St Matthew's Windsor)
You probably have this certificate - if not, it may give some clues as to Jane's parents. Ordering a transcription is cheaper than buying direct. Sometimes, though, early certificates are not much help. The children's birth certificates may also be worth looking at.
There are a couple of mentions on TROVE
http://trove.nla.gov.au/ndp/del/article/13323200 and
http://trove.nla.gov.au/ndp/del/article/28409405These are notices for the death of a Miles LAKE lost off Cape Campbell in the brig Australia - 1873. I assume this is the son born 1830.
http://trove.nla.gov.au/ndp/del/article/2214264 (1837) refers to a parcel of land in Windsor which Miles LAKE left to his widow and which was then sold on.
If Miles was dead by 1837 Jane may well have married again. This seems to be his death - Jane was quite a bit younger than he was.
1832
Miles LAKE, age 57 (V18321894 16)
I note a marriage of a Jane LAKE in 1869 (#433) to a John LINDSAY, registered SYDNEY. This seems a bit late for Jane,
edit to add - and is definitely not her according to the info in a newspaper notice . The only Jane LAKE death I could see was in 1900, which seems a bit late for your Jane.
None of which really helps in finding Jane's parentage.

Judith