Whether the Lut Desert is defined as the hottest desert depends on your definition of "hottest". If you mean the hottest temperature recorded to date, then yes, the Lut Desert has the hottest recorded temperature. However, other definitions of "hottest" may lead us to different answers. For instance, if we define "hottest" as "having hottest average temperatures", then the Lut Desert may not be the hottest. There are also more practical definitions such as wet bulb temperature, which is measured by placing the thermometer in an environment of maximal evaporation.

The concept of wet bulb temperature can be much more useful for humans in terms of survival than dry bulb temperature, which is the temperature we are told from the weather forecast, because wet bulb temperature accounts for the process of evaporative cooling, which is the main ways we cool ourselves when we sweat. the usefulness of wet bulb temperature can be illustrated like this: Suppose we're in a hot but dry place, and we have access to plenty of water. We're not likely to suffer harm in such a place because drinking water and sweating will help us maintain a reasonable body temperature. However, if we are in a humid place that is not as hot as the dry place in terms of dry bulb temperature, we may still suffer physical harm because our sweat would not be able to evaporate as efficiently, and our body temperature would therefore not be regulated as well. To sum up this answer, it depends on your definition of "temperature" and "hottest".

My research says the same thing:
"The single highest land skin temperature recorded in any year of the study was found in the Lut Desert in 2005 and measured a stunning 159.3 F (70.7 C). Lut had the highest surface temperature in 2004, 2006, 2007 and 2009 as well.

While the location of the hottest place on Earth might shift from year to year, the conditions that give rise to it remain the same: Dry, rocky and dark-colored lands are good at absorbing heat, while lighter sand will tend to reflect more sunlight. When comparing natural-color images from Landsat of the Lut Desert to the infrared images, the darker areas show up as the hottest ones."

This is from a good website:
licescience

El Azizia took the record for highest temperature ever recorded on Sept. 13, 1922, when a thermometer on a weather station hit a whopping 136 degrees Fahrenheit (58 degrees Celsius), thanks to southerly winds blowing in hot air from over the Sahara Desert. The sweltering temperature displaced the previous record holder of 134 F, measured at the Furnace Creek weather station in Death Valley on July 10, 1913.

But neither of these places, hot though they may be, deserves the banner of "hottest place on Earth," according to new research by a University of Montana team using data from the U.S. Geological Survey's Landsat satellites.

According to NASA's Earth Observatory website, the Lut Desert currently holds the record of the highest measured temperature, but like everywhere else the Lut Desert fluctuates, and there are other places that have measurements of their own that have come very close, including places in the Taklamakan Desert in China north of Tibet, and even a subtropical shrubland in northern Queensland, Australia.

Finally, there is a difference between the ground temperature and the temperature of the air above it. The ground during the daytime is heated by the sun, and the color of the ground determines how much light it absorbs. A black rock sitting in the sun will be warmer than a white rock sitting next to it.