There would be a new deed in place changing it to your LLC and the lender would more than likely to a modification of mortgage to change the name. 

They are in the process of loan modification and are already 2 months behind in their payment to the loan mod bank.

(and any covid Modifications).  

., the 12-month occupancy requirement for a Primary Residence), andThe Servicer notifies the original owner or natural person that the Mortgaged Premises transferred to an LLC/LP must be transferred back to the original owner or natural person prior to any subsequent refinance or modification application to meet Freddie Mac’s underwriting requirementsThe Servicer has complied with all mortgage insurance requirements applicable to the transferIn connection with any Transfer of Ownership that meets the conditions of this Section 8406.4, a Servicer may not evaluate the creditworthiness of a transferee, require a transferee to assume the Mortgage or otherwise require the Servicer’s or Freddie Mac’s approval of the transfer.

Your current plan without modification is a no-go for me for the reasons @Joe Villeneuve mentioned above.  

For bigger renovations, you need to develop a "standard" format for your process and material selection so that you can easily repeat...but with modifications to suit a different space or desire for an elevated finish.

We left a bookcase over there( we first asked if she is okay with that as it was attached to the wall) and she deattached it and mount big screen TV over there without asking us first as lease says if tenant is going to do some modification, he/she asked to landlord first but she never asked.Please guide me what should i do as lease is year long and i dont know how much will she damage my house .

So, if your REI plan includes anything that might require permitted modification or new construction, i would first determine which jurisdiction the property is in and then go to school on their permitting process.  

If you make significant modifications to the home, you are going to want to be sure the city allows this.

That would expose you to the upside there without necessitating you to move/travel there and REALLY get to know the market.