Lamb is still consumed, but beef more so because it is more available and generally cheaper. I'm not an expert in this area, but I'd recommend reading about ranching on the Great Plains, especially in the period after the American Civil War. For example, the Sheep Wars fought during this time between cattle and sheep ranchers seems particularly relevant. In general, it seems, cattle ranching was better suited to the environment and lifestyle of American ranchers, perhaps because cattle could readily fill the niche left by all those dead bison. Here's another source talking about the development of cattle ranching in that area. Cattle drives from the south up to the rail heads running across Kansas and other areas meant that beef became cheap and available and eventually a staple in the region.
I think you may (unless you have other sources) be confusing the reduction in Sheep livestock since WW2 as a switch in the consumption of their meat.
http://usda.mannlib.cornell.edu/usda/ers/sheeptrends/aib787.pdf
From 7 Million head in the 1800s, sheep numbers peaked at 56million head in 1945, then declined to less than 7 million head January 1, 2003.
At the same time the industry emphasis has switched from wool production to meat production.
Also,there has been a recent measured uptick in consumption, although it appears that per capita consumption is down.
Lamb consumption is very low compared to other meats.
U.S. per capita consumption dropped from 4.5 pounds per capita (retail weight) in the early 1960s to around 1.1 pounds per year over the past two decades.
More than 2 in 3 people don’t consume lamb at all.
Americans eat about 60 times the pork and 90-100 times more beef and chicken each year. In two national cross-sectional surveys reported by the National Research Council, conducted in 1977 and 1985, 1.3 percent of U.S. women and 1.9 percent of men ate lamb. While per capita consumption of other major meats has grown or held steady since then, total lamb and mutton consumption has generally declined since 1975. http://www.border-wars.com/2013/05/the-u-s-sheep-industry-is-belly-up.html
The thing to remember is that the population has increased faster than the increase in consumption.
333 million punds consumed in 1996, to 383 million pounds in 2002.
The US importation of Lamb and mutton has actually increased, with import relief granted to product from Aus and NZ, which has also harmed domestic production.
The Nationwide Food Consumption Survey indicates that...lamb is purchased by fewer than 5% of households on a weekly basis. P16: http://usda.mannlib.cornell.edu/usda/ers/sheeptrends/aib787.pdf
It's very hard to see how people "switched" to other meats, when the consumption of lamb/mutton was never very high anyway.
Consumption of lamb/mutton today is typically limited to older people in several metropolitan areas.
It is also ethnically slanted to immigrant ethnicities which historically preferred the meat over pork or beef.
Meat Packer concentration for lamb, has been limited to specific grographic areas, preventing a more widespread consumption of the meat.
Also, US lamb is grain fed, leading to a slightly more bland product than the New Zealand product which is grass fed.
The primary product from the sheep industry in the US up to the end of WW2 was wool.
Also, it's not easy being a sheep farmer, with 4 large companies controlling the majority of the path of meat from farmers to table.
According to this 2012 NY Times article, farmers (at the time) could expect $0.85 per pound of lamb meat while the price to the consumer was $7 or more at the grocery cash register.
http://www.nytimes.com/2012/12/11/us/drought-and-economic-woes-vex-sheep-farmers.html?_r=0
Another component overlooked is that sheep grazing takes place largely on National Park land.
While cattle are more resistant to this simply due to size, sheepherders are plagued by losses to predators on these National Park lands, and tighter government controls on elimination of predators has exacerbated it.
In some places, the government is re-introducing predators such as wolves to these lands.
Another interesting source for stats. http://www.usda.gov/nass/PUBS/TODAYRPT/shep0213.pdf
One thing to keep in mind: Cattle generally were seen in the old world (Europe, Southwest Asia) as a measure of wealth (hence the word "chattel"), so regular consumption of beef products was a class marker and status symbol in big parts of Europe and the Middle East in pre-modern times. Source: Europe 1320-1450: Hierarchy & Revolt and Feeding the Ottoman Troops on the Danube, 1768-1774, plus other sources that I cannot really recall -- college was back in 2009.
Therefore, I would guess that given the wealth of the new world, consumers chose to consume more status-laden beef rather than less-prestigeous mutton. Also, it should be kept in mind that much of the sheep-raising done in pre-modern times was done for chiefly for textile production -- the meat was an bonus. With the decline in demand for woolen garments in the 20th century, I expect that there was overall reduced demand for sheep products.
As a great deal of recent work in food history has shown, food consumption patterns are often shaped more by social factors than by environmental ones. (hat-tip to /u/agentdcf, who has personally contributed to this area)
Could you perhaps elaborate by what you mean "stop eating lamb?" Do you have a time period in mind and are you comparing North American diets to their European colonizers at the time or just in general?
The decline started in part because of WWII and received a bit of a death blow with the repeal of the National Wool Act in 1996. A few things along the way contributed to the downfall of the industry.
For starters, during the Second World War, the industry began to decline because it was suffering through an important loss of labour from competition with the armed forces and factory work. Then, when G.I.s came back from the war, many of them had had bad experiences with mutton over seas... Mutton had been used in a lot of British mess kits and was of generally poor taste according to American soldiers; preservation for field consumption and preparation being what it was at the time and the Germans used dog meat in a pinch, which was referred to as Blockade Mutton.
Then, most state governments in the 60s started making important changes on the grazing rights on public lands and started legislating on protection for vulnerable endangered species. That made an impact on all farm production in the U.S. but it had an added effect for animal based production: concentration. So, with the combined effects of a change in taste from large swaths of the american public after the war and a major change in the industry during the 60s made a lot of producers switch what they made. Beef and grains were better sellers anyways and the Agriculture Act of 1954 had introduced price support for a bunch of commodities. Althought the National Wool Act came about the same year, it came at a time of change in the taste of consumers so its effects were limited in the following decades.
Another important event is the appreciation of the U.S. dollar during the 1990s against the Australian and New Zealand currencies. Those countries had been consistently beefing up production for a few decades and aggresively subsidized that particular industry. So, the combined effects of imports being cheaper AND American wool and meats being price protected by the Wool Act made American production absolutely noncompetitive. The loss to producers would lead to the death knell that was the loss of the National Wool Act. By the time it was repealed, the damage had already been done and the industry would spiral downwards until 2007 which marks the lowest point ever in American consumption of sheep products.
I has been a long time since I read it, but I think "Horizontal Yellow" by Dan Flores goes into a little detail about the subject. I may be confusing it with another book, though.
