Four back rent payments? Shocking that you didn't get evicted for that.
Of course you can refuse. Presumably, your landlord will keep your security deposit. Assuming your security deposit doesn't cover everything you owe, your landlord may then sue you for the balance. You won't get in any "trouble" beyond that.
Sigh...no, he isn't.
First of all, it's laches (no "t").
Second, I'm assuming you have no clue what laches actually is (nor would I expect you to be familiar with it -- indeed, I don't imagine you ever heard the word before today).
Laches is what's called an equitable defense. It's something that someone who has been sued raises as an affirmative defense. An affirmative defense is something that a person who has been sued and the plaintiff's claim is otherwise meritorious. In your case, you would argue that, despite the fact that you breached the contract by failing to pay rent as agreed and failing to pay late fees pursuant to the lease, you shouldn't have a judgment entered against you because of some reason.
Laches is a defense that says the plaintiff unreasonably delayed in pursuing a legal right and that the delay resulted in prejudice to the defendant. For example, Steven buys property next door to Harold and hires a contractor to begin construction of a house. Harold knows that the house is being built on the property line (and Steven does not know), but he doesn’t say anything. Four years later, Harold and Steven have a disagreement, and Harold files a civil lawsuit, seeking to be paid for that portion of his property that now sits underneath Steven’s house. Steven would argue laches in his defense. Had Harold brought this to Steven’s or the contractor’s attention at the time of construction, the structure could have easily been moved.
In your case, you were aware of the debt and suffered no prejudice as a result of the delay. One could even say you realized a benefit because you didn't get evicted. A delay in suing for money never (or virtually never) results in a valid claim of laches.

