There are a number of Lorenzo Dows - but with additional information such as wife's name or names of children or siblings, it might be easier to trace him.I checked the 1880 census on the familysearch site and found a Lorenzo in North Muddy, Jasper County, Illinois with the following: Lorenzo DOW Self 48 Susan DOWWife 33 Elmedia DOW Dau 12 William T. DOW Son 10 Leanora DOW Dau 8 Lorenzo is listed as b. OH and the rest were all b. IL.
I then checked ths same location on 1870 census and found something that seems to be same family, but age and birth location for Lorenzo are not consistent with 1880.
Lorenzo 24 Susannah 22 Elmeda 1 Maria 12 Rachel 6 This time Lorenzo is listed as b. PA, and the rest were b. IL.
If you e-mail me with some additional details about the Lorenzo Dow family you are researching, I may be able to give you a bit of guidance. Especially helpful would be the surname of his spouse.
And finally, have you checked a death certificate for him to see if it lists his parents' names?