in my master's thesis I made a gram positive DNA extractions . I was Use a method by adding a step with lysozyme at a concentration of 20 mg / ml and incubating 30 min at 37 ° C . ATL and AL buffers must work with gram negative .
In my work I have to identify environmental bacteria's by DNA sequencing and have to extract the DNA of both type bacteria. So first I do the lysozyme lysis (2.0 ul of 100 mg/ml lysozyme) step and then cell lysis solution step for all samples and this works well for both gram positive and negative bacteria. I use kit from jena Bioscience. Hope this will help your work, Good Luck.