From what I can see, as others have said there are only two convicts named Charles Lewis from around that time period
Charles Lewis, trial date 26th May 1819, stole a great coat, transported on Neptune I (2), arrived 16 July 1820. Free certificate (with matching trial date) says native place Chelmsford, baker, blind in right eye.
Charles Lewis, trial date 1st April 1818, stole shoes, transported on Asia (1), arrived 28th December, 1820. Free cert. says - Islington, Tailor (or maybe Sailor?)
I can't see a Charles Lewis on the 1818 Neptune voyage but I can see variation in the muster and census records for the
arrival years stated for both of the convicts above, so I believe that errors were made that led to confusion.
M
Edit - to add links refering to the 1820 Neptune voyage. One of these has Neptune I, II and III to distinguish between three different ships (which I've used), but note that it looks to have been 'Neptune (3)' that was used at the time.
http://www.hawkesbury.net.au/claimaconvict/ship.php?letter=Nhttps://www.jenwilletts.com/ConvictShipsNOPR.htm1826 'Classified Advertising', The Sydney Gazette and New South Wales Advertiser (NSW : 1803 - 1842), 31 May, p. 1. , viewed 01 Jun 2018,
http://nla.gov.au/nla.news-article2185888Edit to add -
His convict indent can also be found on Ancestry, though its only indexed as 'Charles', but can be found by going to the indents database and searching with the conviction date and ship, or see New South Wales, Australia, Convict Indents, 1788-1842, Bound Indentures 1820-1821, image 73
The details agree with those on the free cert.
'Charles Lewis, London Gaol Deliv., 26th May 1819, seven years, Chelmsford, Baker, eyes - hazel blind of right'