What are the environmental conditions for larval Haemonchus contortus to survive?

Lowest temperature

2, 3, 4 and 5 week beakers containing eggs and non-infective larvae in lamb faeces didn't develop into infective larvae (L3) when exposed to fluctuating temperatures ranging from -1 to 15°C:

[...] there were no significant differences in the number of harvested larvae at the different time points for the faeces incubated at 15°C. However, at 5°C and -1 to 15°C no development of eggs occurred, although it was found that a small proportion developed into infective larvae when incubated at 25°C for an extra week. (1)

Highest temperature

Temperature of 40ºC negatively correlated with the survival rates of H. contortus L3. [...] Decreased motility was observed on day 10 after heating. [...] Heating of L3 at higher temperatures (45ºC and 50ºC) caused 100% lethality as early on hour 48 and 24 of exposure (2)

Desiccation

When it comes to dessication, there are three main things to take into account:

• whether the larvae are in exsheathed or ensheathed state matters
• they can survive several dessication/rehydration cycles
• it is best survived below freezing temperatures

The experiments on desiccation survival showed that, after a few hours exposure to 47% R.H., all exsheathed larvae died and all ensheathed larvae survived. (3)

Desiccation protected the larvae against death on storage at temperatures below freezing, but it was harmful at temperatures above freezing. (4)

Ruminant larvae were able to survive up to 7 desiccation/rehydration cycles, and, during anhydrobiosis, metabolic activity was decreased and survival of the larvae was prolonged both in the laboratory and in the field. (5)

pH

The effects of temperature on survival and development of the free-living stages of H. contortus have been studied both by faecal and by agar-culture methods. [...] with a pH range from 6.5 to 8.5 (6)

How long?

As usual, depends on the current environmental variables and current state of the organism and so forth. Read above sections. The article by P. T. Iliev, A. Ivanov, P. Prelezov has a few tables that can give you a good idea of these times (at least for temperature and humidity).

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(1) The development and overwintering survival of free-living larvae of Haemonchus contortus in Sweden, K. Troell, P. Waller and J. Höglund

(2) Effects of temperature and dessication on survival rate of Haemonchus contortus infective larval stage, P. T. Iliev, A. Ivanov, P. Prelezov

(3) Desiccation Survival of the Infective Larva of Haemonchus Contortus, C. ELLENBY

(4) Effect of dessication on the survival of infective Haemonchus contortus larvae under laboratory conditions, Kenneth S. Todd, Jr., Norman D. Levine and Paul A. Boatman

(5) Anhydrobiosis increases survival of trichostrongyle nematodes (abstract only), S E Lettini, Michael Sukhdeo

(6) Trends and Perspectives in Parasitology 2 (page 84), B. A. Newton