Did lanlord give me proper notice to vacate?

If the lease does not, by its terms, automatically renew, then no notice is required. The lease itself is the notice. I would call a tenant's attorney and have them look at it.

As Mr. Skarbek stated, a lease that is on a fixed term ends on the date that is identified (here it is April 4th). A landlord need not give notice, but it is always good practice to give it anyways so that all parties are aware of the other's expectation on April 4th. In some cases, a landlord will remain silent and continue accepting rent. This creates a month-to-month situation, where 30/60 days notice will need to be given to evict a tenant for no-cause. Your landlord has given you an additional month to sort out your move even after the expiration of the lease, which is relatively generous. Had your landlord continued to take your rent without giving you such a notice, then (because you have been there for more than a year), he would be required to give you a 60-day notice to vacate the premises.

Nope--the landlord can give you notice 30 days before the lease expires.