what would be the reason to lie about the unemployment numbers? who reports these and how would lying about them benefit them?

Politicians would like to see the great figures to boast that their policy is working. Chinese GDP statistics were accused by the Indien that they have been manipulated. So that China might be able to show that it is ahead of India, or even the US. In the countries with big informal sector, there are harder to collect statistics. And it might be a lie.

Only president to every actually manipulate unemployment numbers was Reagan.

Before Reagan military members were not counted in employment or unemployment  numbers, Reagan changed that and started counting them, between Active Duty, Reserves and Guard his administration got credited with almost 3 million new jobs without any actually being created.

People who don't want to lose their jobs in an already fragile economy.  It's not like there's anywhere else to go.

As usual, politicians would benefit by lying.  They can't lie about unemployment because the numbers have 100% visibility to hundreds of public agencies, banks and universities that collect the data and do the analysis

There could be motivation to lie about unemployment because it can make the economy look better than it really is. However, the unemployment numbers don't come out of the White House - they come out of the Department of Labor's Bureau of Labor Statistics. The president gets the number only about a day before the public does. There is no reason to believe that the numbers are manipulated. 

Well if you are a sitting President lower unemployment numbers make you look better and make others believe you are doing a better job than you are.

(Repofted) employment stats are the single biggest influence on the stock msrkrt.

Manipulating the numbers made Obama's economy look better