What internet supplier can provide ADSL2 service at Lennox street, Richmond?

You could get iiNet ADSL 2+ at Lennox St, $89.95 gets you 1,000GB per month. I would also look at Optus Cable, they have unlimited data plans now which is so good if you like watching Netflix or internet streaming TV. http://www.iinet.net.au/internet/broadband/adsl/
https://www.optus.com.au/shop/broadband/naked

Whatever you do, don't try Optus ADSL ...absolutely terrible I struggled attempting to download a 1GB update for over 3 hours, connecting the ethernet cable did nothing at all. In the end I gave up and downloaded the same thing via 4G in less than 10 minutes. Since then, I have just used my personal hotspot (1GB a day on Optus prepaid Ultimate for $2 a day - great for general home use, but probably not enough for streaming unfortunately).

Internode, IInet are the best. As of right now, there's no NBN in that street. Being so close to the city, all the major companies will provide it.

I would start with Internode or IInet. Good luck!