Our only reference to the tree known as laurinquë places it in Númenor in the time before the Downfall. There is no record of these trees growing in Middle-earth, so it seems that they would have ceased to exist - at least in mortal lands - with the end of Númenor. Based on its description, the tree seems to have been similar to a laburnum, in which case at least some related trees perhaps survived in Middle-earth. Indeed, though it is never identified as such, laurinquë might conceivably have been a laburnum, in which case it would have survived in Middle-earth after all.
None of this necessarily applies to Aman in the West, from which the trees must have originally found their way to Númenor, and where they would have continued to exist even after the Downfall of Númenor.
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