Python DataFrame Multiple Column Groupby With Max Value From First Group

Data Frame is:

df=pd.DataFrame([[1,'a',30],[1,'b',60],[1,'b',40],[2,'g',40],[2,'g',9],[3,'k',20],[3,'k',69],[3,'k',29],[3,'f',99]], columns = ['Lot','Item','Date'])

     Lot Item  Date
0    1    a    30
1    1    b    60
2    1    b    40
3    2    g    40
4    2    g     9
5    3    k    20
6    3    k    69
7    3    k    29
8    3    f    99

I need to

  1. Group By Lot and then Item
  2. Get the First Item in each Lot
  3. Finally Get the Max Date for each First Item GROUP in Each Lot

The OUTPUT should be:

     Lot Item  Date
0    1    a    30
3    2    g    40
6    3    k    69

Thank you !!!