What is the manufacture date of a marlin serial number LTD00681?

Click on this link to look up year. oldguns.net/sn_php/marlinlookup.php Yours is a 1982 model year (18132229)

I would say that your marlin was made in 1899 if it is a model 1889,1891,1892,1893,1894,1897.I would say that you would probably have a marlin 1893 even though you do not state this in your question.

With the serial number that you provided,your Marlin rifle was produced in the year 1979.

1893

1883.