import pandas as pd

# Create a DataFrame
df = pd.DataFrame({'A': [1, 2, 3, 4]})

# Create a column doubling the values of column A
df['B'] = df['A'] * 2

# Apply lambda function to column A to create column C
df['C'] = df['A'].apply(lambda x: x ** 2)

# Print data frame
print(df)

>>>

   A  B   C
0  1  2   1
1  2  4   4
2  3  6   9
3  4  8  16