Many years since I did this walk. It's a nice enough walk as long as not too hot as it's all on fire trail. Blue Gums along there are really good.
From memory it's only about 2 km of dirt road to the locked gate trackhead from the southern entry to Thirlmere Lakes NP via Slades Road.
Looks like you have to go in that way at present in any case, as Slades Road is closed between West Parade and Dry Lakes Road according to NPWS alerts.
The walking track around the lakes is also currently closed.
My recollection is that there were potholes etc on that road and a fair bit of standing water after rain. It's a long time ago but in more recent years when I've visited the lakes the road has been similar.
It gets used a lot by people just going there for picnics etc. I've always owned 4WDs or AWDs but 2WD should be OK with care.
From NPWS site it appears they have upgraded the trackhead/car park, it used to be just a locked gate and little else. Plenty of current info here:
https://www.nationalparks.nsw.gov.au/things-to-do/walking-tracks/couridjah-corridor-walk