Journal entry for liability

According to me for first situation relates to prior period and thus will be accounted as per AS-5

For Sit.1

Lease Rent A/c Dr.

To Prov. for Lease rent

the amount will be shown in P&L as prior period item

For Situation 2 is the liability crystalise or in dispute (since you have received notice) if its crystalise, account it as prior period or if it is in dispute show it as contingent liability

As said by Mr. Yusuf. if it is crystalized, then pass entry and show it under prior period item in P&L.

if there is any dispute show it as contingent liability under the B/S