Both are correct and would be used by a native speaker. "Lots of time" is slightly more informal.

Your "friend" in the US is not so accurate as he or she may think. I have lots of time to answer your inquiry. I have a lot of time to answer questions. Lots of time is available to us at this particular moment. In an hour or two, there may not be a lot of time available to us. . If there is a lot of time available to us, we can discuss these subject at length; but I am not sure if you will have a lot of time to discuss this with me. There is a lot of time for study if one is a full time student; but a person holding a full time job may not have lots of time for study. Also Cathy, you can use other phrasing, and avoid the difficulty of choosing the phrases you cite here. You can say or write, for example: "There is ample time available to us." or "There is sufficient time available to us to accomplish this task." or "There is enough time to get all of these things done." or you might write or say; "There is not enough time to get all of this work done." There is not an adequate amount of time available to us." or "There is less time available to us than I thought." "There just is not enough time to do all of this work." If there were more time, we could get more studying done; but there just is not enough time in a day to complete all of these lessons. Do you think there will be enough time? I do not think there will be enough time. Do you have a lot of time, or only a little time to talk to me. You seem to have a lot of free time. You seem to have lots of free time. I have lots of time at the moment and probably much more free time than you have.

친구... They are not both slang. A lot is proper English. Lots is slang. Lots should never be used in formal writing. Americans use lots a lot! :(

Thanks Garrett!!! I really appreciate your help :D I'm so happy to hear that!!!

Both are fine. Both are slang anyway, so I don't think it really matters which one you use. In formal papers, you should try to use other words such as "many" "an abundance" "several" etc. Some people just have preferences, so that's maybe why your friend corrected you Why didn't you ask your friend why he corrected you? Haha You will find that many Americans don't speak/write properly so it's not always good to believe/follow one person :P So be careful who you learn from haha I speak pretty well for the most part, so you can ask me if you have any questions like this in the future. If I don't know the answer, I can find out for you.