I listened to it and don't recall Lodsys coming up. The shell company in the story was called Oasis. In court filings they were forced to disclose that Intellectual Ventures was getting 90% of their proceeds (which were considerable—hundreds of millions) from troll lawsuits.
A plainer way of putting this is that IV outsources its dirty work for a 10% cut while retaining plausible deniability.
They would have gotten away with it in the Oasis case, except that a couple of brave victims fought back and (as the broadcast told it) were saved by a fluke: a document from 20 years ago that contradicted the patent filing. The patent wasn't invalidated because it was laughable, but because the "inventor" lied about it being all his idea.
Since IV has a similar murky connection to Lodsys' patents as to Oasis', and since they have put out the same non-denial-denial verbiage about both entities, and since we now know that they were taking 90% of Oasis' winnings all along, it's reasonable to suspect that they have an analogous deal with Lodsys. But this hasn't been demonstrated. The OP is arguably being a bit of a troll by titling his piece as if it has, then adding the word "allegedly" in later.
It's widely believed that Lodsys is somehow affiliated with Intellectual Ventures, but US corporate law makes it hard to really know who owns or benefits from Lodsys' lawsuits. Intellectual Ventures is known to participate in a lot of shell corporations and intellectual property trades. EFF notes that Intellectual Ventures used to own some of the patents Lodsys is prosecuting: https://www.eff.org/issues/faqs-lodsys-targets
> US corporate law makes it hard to really know who owns or benefits from Lodsys' lawsuits
As the director of a UK company every time I here this I am simply flabbergasted. In the UK all limited companies/partnerships accounts are a matter of public record.