What is accounting treatments in Lease hold improvement? how to depreciate it..?

In my opinion, leasehold improvement should be accounted as Assets. I will suggest to depreciate the cost on monthly basis during the initial lease term or maximum5 years whichever lower.

When you pay for leasehold improvements, capitalize them if they exceed the corporate capitalization limit. If not, charge them to expense in the period incurred. If you capitalize these expenditures, then amortize them over the shorter of their useful life or the remaining term of the lease. The remaining term of the lease for amortization purposes can be extended into additional lease renewal periods if the renewal is reasonably assured (such as when there is a bargain renewal option).

If you subsequently purchase the building, the lease is presumably dissolved, so you can then amortize over the estimated remaining useful life of the building, which is likely to be a much longer period than the term of the original lease, resulting in a significantly smaller monthly charge.