Is this grammatically correct as written, or do I need to change commas, italics, apostrophes, or quotation marks?
"Yes," I replied, "but I don't have the original recipe; therefore, lets use one in the "Favorite Home-Baked Breads" chapter of Today's Cooking Fifty Easy-to-Follow Recipes."
The grammar of your quotation, the words used and the agreements of tenses and so forth, is fine. The punctuation, however, needs some revision.
A semi-colon is used between two independent clauses. You could leave the semi-colon where it is, but it might be more appropriate to use a period there and capitalize the first word of your new sentence.
You need an apostrophe to show the contraction of "let us."
In order to set off the title of your resource cookbook, you should use an italic font for the entire title. There probably should be a colon in the title to indicate that there are a collection of recipes included in the book.
This means that your corrected quotation would be:
"Yes," I replied, "but I don't have the original recipe. Therefore, let's use one in the "Favorite Home-Baked Breads" chapter of Today's Cooking: Fifty Easy-to-Follow Recipes."