Distance: 2.7 km (2.5 DOC hours) - Unmarked route, clear - Moderate terrain
Altitude: 1306m to 1791m. Gain: 29m. Loss: 510m . Gradient: 12 deg (Moderate-hard)
Skills: Occasional scrambles (3/7) - Streams (2/6)

Unmarked route, clear (7/9)
Unmarked route, follows obvious geography (river, spur, trail, etc)

Primary, unmapped (2/5)
Route not on maps, but is principal access to hut or along range / catchment

Moderate-hard (difficulty: 4/5)
Continuous moderate climbs

Moderate (difficulty: 3/5)
Low scrub in open or bush / river rocks

Occasional scrambles (difficulty: 3/7)
Tramp with some scrambles and exposure to falls

Streams (difficulty: 2/6)
Small streams, danger only in extreme weather

Unknown (difficulty: 0/7)
Not specified

(notes from duplicate route by @millera)

Lake Thompson is a majestic setting and a lovely place to camp in good weather. I would describe it as slightly smaller than Lake Angelus, in a similar majestic mountain setting, but without the hut and people.

The descent from Lake Thompson begins down the obvious earthquake scarp to the west of the lake (Figure 18a) – avoid exiting from the main stream draining the lake, as this leads to bluffs and waterfalls. The descent became a narrow valley, which then became steep with vertical drops after turning east (Figure 18b). I made for the ridge to the true left (Figure 19a) which gave easy walking all the way down, re-joining the river close to the Waiau Pass turnoff. This is the beginning of the marked route, part of the Waiau Pass route and the Te Araroa Trail (Figure 19b).

Note: Described in the reverse direction to your journey

Crossing the river to the TR, we tried to cut the corner but travel was easier closer to the stream.

Crossing back to the TL involved a scramble down and up out of the stream. Then a stiff climb to the gut (and fault line) that runs up to Lake Thompson. We traveled in the gut but travel would also be good on the ridgetop. From Lake Thompson, it's a short climb to Thompson Pass, first on a grassy tongue, then on rock.