When the refundable deposit is given to lessor, the lessee records a receivable, when it's returned, the lessee simply credits the receivable.

For non-refundable deposit, when it's earned by the lessor, the lessee debits expense and credits prepaid rent expense. So it seems that lessee doesn't really amortize the deposit unless in the fact pattern it says that's how the deposit gets earned. I guess.

check the entries for sales-type lease and direct financing lease.

The lessor of a sales-type lease records a sale, that sale is the selling price, which is also the PV fo minimum lease payments;

The lessor of a direct financing type lease debits the lease pmt receivable and credits the asset which is at PV of the minimum lease pmts.