Lulu rents an apartment for $300 a week. After a year, Lulu gives notice that she is to move to a cheaper apartment. The landlord asks Lulu to stay and offers her rent of $100, which she accepts. The landlord says not to worry about changing the lease, as he is a man of his word'.

After one year of paying less rent, Lulu decides to relocate to another country and gives notice of leaving. The landlord demands outstanding rent, which is the difference between the $100 a week she paid, and the amount she would have paid for the $300 a week apartment according to the lease.

Can the landlord demand the full rent stated on the lease? Explain Lulu's rights under the law, using cases to support your answer