When I want high recovery of genomic DNA I start by treating the cells with lysozyme. To that end I include the instructions from Sigma lysozyme pdf referred to in link below and also attached
Once you have incubated with lysozyme you can then proceed with extraction according to SOP provided with your Sigma genomic extraction kit
As @LaurenceStuartHall mentioned, lysozyme works really good to me. Maybe you can try using other protocol because sometimes using a kit is not really helpful and they're a quite expensive.
A simple method for the isolation of chromosomal DNA from gram positive or acid-fast bacteria. C Bollet, M J Gevaudan, X de Lamballerie, C Zandotti, and P de Micco
Indian J Microbiol. 2010 Oct; 50(4): 412–418.
A Simple Method for the Efficient Isolation of Genomic DNA from Lactobacilli Isolated from Traditional Indian Fermented Milk (dahi)
Sachinandan De,corresponding author1 Gurpreet Kaur,1 Amit Roy,1 Gaurav Dogra,2 Ramakant Kaushik,1 Paras Yadav,1 Rameshwar Singh,2 Tirtha Kumar Datta,1 and Surender Lal Goswami1