Here it is a few questions.

1) I have lived there the last year. (2009) EQUALS I lived there last year. (2009) (Yes/No)

2) I lived there last year. (2009) DOESN’T EQUAL I lived there the last year. (means the last year of some period in the past)(Yes/No)

3) I have lived there the last 5 years. EQUALS I have lived here these 5 years. (Yes/No)

4) I have lived here in the last 2 years.Does it mean 2 years (365 days + 265 days) back from the moment of speaking? It doesn’t mean 2 calendar years, does it?
First: You specifically asked for 'yes/no' answers. I gave you full measure.
Second: I am a busy man. I try to help many people, and I do that by giving a sufficient answer but no more. If more information is required, you should ask for it, not sit back and wait for a lengthy elucidation. I am not paid by the hour.

1-- Yes, that is the difference.

2-- Of course; you should have recognized that before you posted.
1-- No, they are not 'equal'

2-- No, they can be 'equal'.
3-- Yes
4-- It means at some time during the last two years; it could have been for only a month.
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Thanks for dropping me a coin of your attention)))))) I like your way of explaination, however, it has become a bit too concise lately. Is it a shortage of time or a lack of desire to disclose the "hidden mysterious" of the English grammar? I hope you are not offended by my inocent humor. On the serious note, let me get back to the point........

1) What makes them different? Imagine that it is 2010 now. Do they refer to 2009?
I have lived there the last year. (2009) I lived there last year.
(If the only difference is about the perfect and simple i.e. I have lived there the last year. (I still live here) and I lived there last year (I don't live here any more) then I see the difference. If there is another difference, please, point it out)

2) The can be equal ONLY when the previous year of the present one coincide with the last year of a certain period in the past, right? Like

The factory was closed in 2010 and I worked there the last year (which means 2009-2010). In this case it will coincide with I stopped working there last year which is also 2009.
 Mister Micawber's reply was promoted to an answer.