It seems to me that if Aaron looked on FBMD then probably none if the references he gives are the right one. Not if you actually have the birth date as Aug 13 1865! If look at the coverage charts for FBMD they only have about 65% of the data for 1865 in the database so far.
You can check online at
http://www.1837online.com/Trace2web/It costs something to use it and you can order the certificates through them.
Alternatively, I have used the following site
and he will take cheques in dollars though obviously it will slow the process down as it will involve posting it. He will search the GRO for a small charge if you are not sure of the dates. I got very good service from him.
I don't understand why he is not in the 1881 census (I think the one given before is clearly the one born in 1860 at Caistor and a very poor fit if yours was born in 1865). There is however one born 1866 at Doncaster which is not far from the Lincoln border AND his parents both give their birthplaces as Lincoln. Or he could just be missing as my gtgrandfather is even though I know pretty much where he was at the time.
Apologies for jumping in here, I just think you should be cautious. If you are certain of the birth date I would try the certificate site I gave you. If not try either them of the 1837 one. Good luck!