Many ordinary people in Western countries do and will have [investments in AI/robots] (if only for retirement purposes), and will therefore receive a fraction of the net output from the robots. 

... Of course, many people today don't have such investments. But under our existing arrangements, whoever does own the robots will receive the profits and be taxed. Those taxes can either fund consumption directly (a citizen's dividend, dole, or suchlike) or (better I think) be used to buy capital investments in the robots - such purchases could be distributed to everyone.

...Given the potentially immense productivity of zero-human-labor production, even a very small investment in robots might yield dividends supporting a lavish lifestyle.

I appreciate the nuance.  

My takes:

• Yes, I would also expect many non-tech-people in the Global North to invest in AI-based corporations, if only by investing savings in an (equal or market-cap weighted) index fund.
• However, this still results in an even much stronger inequality of incomes and savings than in the current economy, because in-the-know-tech-investors will keep reinvesting profits into high-RoI (and likely highly societally extractive) investments for scaling up AI and connected machine infrastructure.
• You might argue that if most people (in the Global North) are still able to live lavish lifestyles relative to current lifestyles, that would not be too bad. However, Forrest's arguments go further than that.
  • Technology would be invested into and deployed most by companies (particularly those led by power-hungry leaders with Dark Triad traits) that are (selected by market profits for being) the most able to extract and arbitrage fungible value through the complex local cultural arrangements on which market exchanges depend to run. So basically, the GDP growth you would measure from the outside would not concretely translate into "robots give us lavish lifestyles". It actually would look like depleting all what's out there for effectively and efficiently marketing and selling "products and services" that are increasingly mismatched with what we local humans deeply care about and value. 
    • I've got a post lined up exploring this.
  • Further, the scaling up of automated self-learning machinery will displace scarce atomic and energy resources for use for producing and maintaining the artificial robots in the place of reproducing and protecting the organic humans. This would rapidly accelerate what we humans started in exploiting natural resources for our own tribal and economic uses (cutting down forests and so on), destroying the natural habitats of other organic species in the process (connected ecosystems that humans too depend on for their existence). Except, this time, the human markets, the human cultures, and the humans themselves are the ones to go.