Early termination of a tenancy contract with a notice period

Dear sir/madam,

My tenancy contract expires on 17.07. 2020. On 22.12.2019, I emailed the owner with a termination of the contract to be on 31.03.2020.

The contract says:

The Lessee may terminate Contract and vacate Premises following the Labor's written consent and upon Lessee agreeing the following:

(a) Provide at least two months written notice to the Lessor prior to the expiry of the Term of its intention to vacate the Premises where such notice once served cannot be retracted unless the Lessor provides its written consent;

(b) Settlement of the Lessors administration fee currently in force for breaking the Contract prior to the expiry of the Term, subject to the Lessor's approval. The Lessor is not obliged to refund to the Lessee any difference in rent in case of an early break of the Contract.

The owner says that this notice period is applicable only to non-renewal, not early termination so either to pay penalty or complete till 16.07.2020.

Is this true? Is there a limit to the penalty to 2 or 3 months or can they ask for more?