after a long time, especially when there has been some difficulty or delay synonym eventually. The performance finally started half an hour late.

There are three meanings listed in OED's entry for the adverb finally. See 'Meaning & use' for definitions, usage, and quotation evidence.

[only before noun] being or happening at the end of a series of events, actions, statements, etc. his final act as party leader; Jamie is in his final year ...

finally adverb (AFTER TIME) ... after a long time or some difficulty: We finally got home at midnight. After months of looking he finally found a job.

at the end of a period of time or a series of events. Use finally for the last in a list of things: Finally, I'd like to thank my parents.

Lastly is used to introduce the last in a list of things or the final point you are making. Lastly, I would like to thank my parents for all their support.

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.

1[only before noun] being or happening at the end of a series of events, actions, statements, etc. · 2[only before noun] being the result of a particular process ...

the last of a series of games or competitions in which the winner is decided. She reached the final of the 100m hurdles. The players met in last year's final.

Putting an end to something (rarely const. of, to); putting an end to strife or uncertainty; not to be undone, altered, or revoked; conclusive. Formerly often ...