Python // Pandas // Apply - Lambda function with multiple if statements

I'm trying to infer a classification according to the size of a person in a dataframe like this one:

      Size
1     80000
2     8000000
3     8000000000
...

I want it to look like this:

      Size        Classification
1     80000       <1m
2     8000000     1-10m
3     8000000000  >1bi
...

I understand that the ideal process would be to apply a lambda function like this:

df['Classification']=df['Size'].apply(lambda x: "<1m" if x<1000000 else "1-10m" if 1000000<x<10000000 else ...)

I checked a few posts regarding multiple ifs in a lambda function, here is an example link, but that synthax is not working for me for some reason in a multiple ifs statement, but it was working in a single if condition.

So I tried this "very elegant" solution:

df['Classification']=df['Size'].apply(lambda x: "<1m" if x<1000000 else pass)
df['Classification']=df['Size'].apply(lambda x: "1-10m" if 1000000 < x < 10000000 else pass)
df['Classification']=df['Size'].apply(lambda x: "10-50m" if 10000000 < x < 50000000 else pass)
df['Classification']=df['Size'].apply(lambda x: "50-100m" if 50000000 < x < 100000000 else pass)
df['Classification']=df['Size'].apply(lambda x: "100-500m" if 100000000 < x < 500000000 else pass)
df['Classification']=df['Size'].apply(lambda x: "500m-1bi" if 500000000 < x < 1000000000 else pass)
df['Classification']=df['Size'].apply(lambda x: ">1bi" if 1000000000 < x else pass)

Works out that "pass" seems not to apply to lambda functions as well:

df['Classification']=df['Size'].apply(lambda x: "<1m" if x<1000000 else pass)
SyntaxError: invalid syntax

Any suggestions on the correct synthax for a multiple if statement inside a lambda function in an apply method in Pandas? Either multi-line or single line solutions work for me.