I know that some plants die for old age like a lettuce. But there are trees like Baobabs or larger Ficus in the tropics of whom we don't know their age. And trees like spruce reaching 9950 years old, which die for environmental factors and not by age.
However, E.g. when we multiply vegetatively an olive or cacao tree, we use a fragment or clone from a unique individual passing the same genetic information, again and again.
Then, can these plants live forever?
The answers to these questions often boil down to "what do you mean by live forever?".
You've included vegetative cloning, so I infer that counts as one living organism for your purposes. In that case, the answer is absolutely.
Pando is at least 10 thousand years old and only getting larger. The Cavendish banana is about 150 years old, but produces at least 70 million tons of bananas yearly.
See here for other giant clones. Of particular interest is King's Lomatia, represented as a species by a single, sterile, individual. Fossilized triploid leaves are too old for carbon dating(at least 45 thousand years old), so it's essentially unknown how old it is.
I would be comfortable declaring Pando immortal, since it's way too big to be eaten, too resilient to burn down, and has already survived the middle and end(at least!) of an ice age. That just leaves (ha) disease and basically nothing else as possible threats.
Forever no. For thousands of years yes. And not only plants, other organisms have what is called biological immortality. Look here for some examples https://en.m.wikipedia.org/wiki/List_of_long-living_organisms
