I'm no microbiologist but I'm sure pure lactose (or any other sugar) cannot be a sufficient substrate for growing L Reuteri. It needs protein as a source of nitrogen. That's why we heat the milk to denature the proteins in it and thus make them more available for digestion by the L Reuteri.
If you look back through the thread you'll see that another poster was experimenting with a non-milk substrate - I forget his handle.
Really? Hmmm.... the NItorgen part is a surprise to me. If so -and may very well be the case- there is very minimal amounts of nitrogen needed, because when transitioning from a specific amount of milk to yogurt, there is essentially no loss in total protein weight as far as I know.
Also, yes people have tried all sorts of alternative culturing mediums, but in every case I have read taste was a consdieration; nobody wanted to end up with a concoction that ended up tasting like garbage. Not all the ingredients used were claimed to be essential for the fermentation process.
In my case, I am OK with a very foul tasting mixture; if I succeed it will taste very bad perhaps. It will be water, that is nastily sweet due to the lactose, theeafter made sour by the lactic acid.