Finally, at last, lastly and in the end all have a meaning of ‘after a period of time’. However, we use them in different ways.
We use finally to refer to something that happened after a long time and usually after some difficulties. In this meaning, finally most commonly occurs in the normal mid position for adverbs, between the subject and the main verb, after the modal verb or the first auxiliary verb, or after be as a main verb:
There were no taxis and we finally got home at 2 pm.
She’s had over twenty interviews but Jasmine has finally got a job as a journalist.
We use at last when we have been impatient as a result of long delays. Like finally, at last occurs in the normal mid position for adverbs as well as in front and end position:
At last I’ve discovered how to print envelopes on my printer!
She has at last given me the book she promised me.
They’re here at last!! We’ve been waiting half an hour.
We use lastly to refer to something that comes at the end of a long list:
We need eggs, milk, sugar, bread and, lastly, we mustn’t forget yoghurt for Dad.
I’ve thanked my parents but lastly I must thank all my friends for their help.
In the end
We use in the end to refer to a conclusion after a long process, after a lot of changes or after a lot of discussion:
We were going to ski in Austria, then the South of France and in the end we decided to go to Italy.
And then, in the end, after months of discussion they offered to buy our house.