I can think of several ways to pursue this.
First, the National Archives Records of Scotland will almost certainly have the records of the bankruptcy proceedings, so have a look in their catalogue at
www.nas.gov.ukSecond, I would go to
www.scotlandspeople.gov.uk and look for Andrew Lindsay in the 1861 census. He is bound to be there somewhere, because the census was taken six months before the bankruptcy notice. The census will tell you how old he was, where he was born, and if he was married it will tell you the names, ages and birthplaces of his wife and children. Then look for him in the 1871 census. If he is still to be found in Scotland, then he is obviously not your one.
If he did have a family in 1861, use the 1861 census information to look for the birth dates of the children at
www.familysearch.org. If one of them was born in 1855, get that birth certificate from
www.scotlandspeople. It will give you a wealth of information about the family, far more than earlier baptism records or later birth certificates.
One other avenue you could pursue would be to look in 19th century newspapers for reports about the bankruptcy proceedings. Some, but not all, issues of the Glasgow Herald can be browsed online - I have apparently mislaid the URL but someone else will know and will tell us - and the Scotsman Digital Archive is available through the Gale 19th century Newspaper Collection
http://gdc.gale.com/nineteenth-century-collections-online/ fully indexed or at
http://archive.scotsman.com , both of which are subscription sites.