I agreed via e-mail that I would give the owner 45 days notice when moving out. However, on my LEASE, it only states that either party only needs to give 30 days notice.

I only gave 30 days notice and my landlord is keeping half of the deposit (he is an attorney btw). Can he do this even though the lease states 30 days is sufficient. Am I bound to my e-mail agreement? Which was informal btw; I just said "Sure, I will give you one and a half months notice when I move".

I agreed via e-mail that I would give the owner 45 days notice when moving out. However, on my LEASE, it only states that either party only needs to give 30 days notice.

I only gave 30 days notice and my landlord is keeping half of the deposit (he is an attorney btw). Can he do this even though the lease states 30 days is sufficient. Am I bound to my e-mail agreement? Which was informal btw; I just said "Sure, I will give you one and a half months notice when I move".

Whether it is transmitted by first being printed, and then sent via the U.S. mail ("snail-mail"), or not printed but nevertheless transmitted electronically to the intended recipient ("e-mail") is immaterial. The important thing is the legal effect of the writing.

This e-mail you sent might be (whether or not it was "informal") regarded as the embodiment of an agreement to modify the contractual terms of the lease. Depending upon the circumstances, you might possibly argue that your landlord gave no consideration and that therefore there was no agreement (or contract) to modify the original terms of the lease. However your landlord could very well argue that, consideration or not, he relied upon your promise to give 45 days notice, that he relied upon this promise to his detriment. This is called "promissory estoppel", and may possibly form the basis of his claim.

Another issue would be whether the deposit may be used to compensate him for (arguably due and) unpaid rental payments. That would depend upon the terms of the lease and the law of whatever jurisdiction you are in.

Thanks for your help! However, I made the agreement via email before signing the contract which means that the e-mail was not intended to modify the lease. Right? I signed the lease after the agreement. Does that make any difference?

Does it make a difference that I only stayed for 2 weeks after I gave 30 days notice? I actually lost money but I still gave 30 days notice (I had to move out sooner). So he has time to find a tenant; it's not like I left him high and dry.

Also, this is the exact wording in the e-mail

He wrote "Can you give me at least a month and half notice if you move out, so I can find another good room mate. That's all I ask for."

I wrote " I will give you a month and a half notice when I do move."

Which was written before I signed the lease which states 30 days

Thanks for your help! However, I made the agreement via email before signing the contract which means that the e-mail was not intended to modify the lease. Right? I signed the lease after the agreement. Does that make any difference?.
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It certainly does. In that case, normally the law holds that if the agreement (the lease) contained all of the essential terms of the contract (if it was an "integrated" agreement in lawyers' terms), different provisions (such as the 45 days discussed in your e-mail interchange) do not become part of the contract. If he wanted 45 days, he should have made sure that the contract said 45 days.

Thanks so much for your help !

While I agree with AK, if you want to fight this you will need to go to court. It may not be worth the time and hassle.