Every life has a lifespan
I was going to say 'no, there are immortal organisms', but then you mentioned it yourself!
The chances I guess are slim that we'll see immortal humans in our life, but I do believe humans will definitely discover biological immortality in the future, probably the relatively near future (even a thousand years is objectively nothing).
Sure, lots of money and work is invested into researches to elongate human lives and while it could be possible in the future, currently, we just have to live our best lives not falling for cosmetic companies selling us the best product to look young.