Используйте функцию stack()
#Creating DataFrame
df=pd.DataFrame({'FID':[0,1,2,3,4],'Lat':[51.62,51.62,51.62,51.62,51.62],'Lon':[-63.81,-63.80,-63.80,-63.80,-63.80],'23-May':[-.04,-.05,-.05,-.06,-.05],'18-May':[0.08,0.09,0.08,0.08,0.09],'25-May':[.1,.1,.07,.11,.11],'28-May':[0.13,.13,.12,.14,.16]})
df=df[['FID','Lat','Lon','23-May','18-May','25-May','28-May']]
df
FID Lat Lon 23-May 18-May 25-May 28-May
0 0 51.62 -63.81 -0.04 0.08 0.10 0.13
1 1 51.62 -63.80 -0.05 0.09 0.10 0.13
2 2 51.62 -63.80 -0.05 0.08 0.07 0.12
3 3 51.62 -63.80 -0.06 0.08 0.11 0.14
4 4 51.62 -63.80 -0.05 0.09 0.11 0.16
df_stacked=df.set_index(['FID','Lat','Lon']).stack().reset_index()
df_stacked=df_stacked.rename(columns={'level_3':'Date',0:'Value'})
df_stacked=df_stacked[['FID','Lat','Lon','Value','Date']]
df_stacked
FID Lat Lon Value Date
0 0 51.62 -63.81 -0.04 23-May
1 0 51.62 -63.81 0.08 18-May
2 0 51.62 -63.81 0.10 25-May
3 0 51.62 -63.81 0.13 28-May
4 1 51.62 -63.80 -0.05 23-May
5 1 51.62 -63.80 0.09 18-May
6 1 51.62 -63.80 0.10 25-May
7 1 51.62 -63.80 0.13 28-May
8 2 51.62 -63.80 -0.05 23-May
9 2 51.62 -63.80 0.08 18-May
10 2 51.62 -63.80 0.07 25-May
11 2 51.62 -63.80 0.12 28-May
12 3 51.62 -63.80 -0.06 23-May
13 3 51.62 -63.80 0.08 18-May
14 3 51.62 -63.80 0.11 25-May
15 3 51.62 -63.80 0.14 28-May
16 4 51.62 -63.80 -0.05 23-May
17 4 51.62 -63.80 0.09 18-May
18 4 51.62 -63.80 0.11 25-May
19 4 51.62 -63.80 0.16 28-May