LBM and workouts (JMBR)- concerned

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So I am new to actually being healthy. I use to be skinny (the coffee, smoking, no car, or money for food diet). Slowly gained, but now I am trying to do this all right. My confusion currently is how to retain as much LBM while at a deficit. I am doing jillian michaels Body Revolution until my youngest can do gym daycare. I push myself and use as heavy of weights I can use without messing up form. I am sore after each workout so I personally feel like I am challenging myself and my body. Is this type of training enough to help keep some LMB? Is there anything else I should do that can be done at home? I get I cannot gain muscle at a deficit. I know this has been asked 1000 times and I may have used terms or concepts wrong (feel free to correct me!). My eating is still not great, but i am getting there! Thanks for any input.