Welcome Lydia, I hope you could find Arabic easy.
Look Lydia! 1) لم يكن basically is the negative past form of كان, to get the present form we would say لا يكون and this is a rule. 2) When you conjugate a verb to the negative present then you must put the present tense along side with لا, not لا with the past tense, that is because in Arabic the basic tense is the past tense not the present as in English, therefore we start from the past as the most basic and simple form and then conjugate the other tenses from it.3) However there is one situation "as I know" we could use لا with the past tense and we'd use it if we want to hope that something didn't happen will not happen also in the future (I hope I made it clear here :) ), this is generally aggressive and somehow with showing anger. I will give you a punch of easy examples right now-with the same system of numbers I used (1,2,3):
1) "لم يكن الامتحان صعبًا" "The exam was not difficult"
"لم يكن الولد غاضبًا" "The child was not angry"
"لم تكن الفتاة عالمةً" "The girl was not a scientist" ....
2) "لا يكون الرجل الحقيقي كاذبًا" "The real man can't be a liar"
" لا يذهب الطلاب إلى المدرسة" "The students don't go to school" here I used another verb to clarify the idea and this verb is ذهب - يذهب.
"لا يكون الثلج صلبًا" "Snow isn't solid"...
3) "لم يكن لدينا مالٌ كافٍ" - "لا كان" "We didn't have enough money" - "Hopefully you will not ever".
"لم يستطعْ أن يفعلَ ذلك" - "لا استطاع" "He couldn't do that" - "Hopefully he will not ever " this means I hope he will not ever be able to do so, then he will not have the ability, he will be disabled. And here I used another verb which is استطاع-يستطيع.
I hope I could make it clearer and more obvious for you :) .