I think they're mostly funded by a Belgian venture capital group called Genii, I'm sure I'll be corrected if I'm wrong, and that Renault have been decreasing their involvement with a view to pulling out altogether. Lotus cars were funding them but pulled out unexpectedly causing a bit of a crisis for the team at the time.
The way I see it is that I doubt any F1 fan thinks they have any DNA of the Chapman team but I like to see the name still around. I see them as totally separate from the heritage of the original Lotus and, having struggled to survive and to surmount the scandals of the Briatore years, they are now forging a new identity.
I think that when Lotus Group were funding them, Lotus Group were waging a very aggressive and personal war with Tony Fernandes's team and were determined to win and take the name from him. But as I understand it, all that remains from that liaison is the name as Lotus Group dropped the team just as swiftly as they arrived, under orders from parent company, Proton; I think it ended up this way more circumstantially really.