How would I style a column's elements based on another column's elements in a pandas data frame?

Say, for example, I have a pandas data frame like so:

import pandas as pd

# Sample DataFrame
data = {
    'Greek letters': ["Alpha", "Beta", "Gamma", "Omega", "Delta"],
    'English letters': ["A", "B", "C", "D", "E"],
    'Greek Letter score': [5, 10, 15, 20, 25],
    'English Letter score': [3, 11, 12, 18, 25]
}
df = pd.DataFrame(data)

What I want to do is apply specific background colors only to the elements in the columns Greek letters and English letters based on their respective scores (so, based on the elements in the Greek Letter score and English Letter score columns respectively).

def highlight_letter(value):
    # How would I use the letter element to obtain its corresponding score?
    # score = some technique to obtain the letter's score 
    if score <= 10:
        return 'background-color: lightgreen'
    elif score <= 20:
        return 'background-color: yellow'
    else:
        return 'background-color: blue'

styled_df = df.style.applymap(highlight_letter, subset=['Greek letters', 'English letters'])

This is what the expected output should look like:

Actually, what you need is not applymap but apply along the rows. To avoid hardcoding, let's assume that you have at least pairs like "Something letters" and "Something Letter score" in whatever case and column order it can be. With that in mind, I'd suggest this approach:

def highlight_letter(record):
    formatting = record.copy()
    subset = record.index.str.endswith('letters')
    formatting[~subset] = ''
    for name in formatting.index[subset]:
        score = record[name[:-1] + ' score']   # -1 to drop ending s in letters
        formatting[name] = (
            'background-color: lightgreen' if score <= 10 else
            'background-color: yellow' if score <= 20 else
            'background-color: blue'
        )
    return formatting


styled_df = df.rename(columns=str.lower).style.apply(
    highlight_letter,
    axis='columns'
)

The output on your test data looks like this:

Update

Here's another way for the case where we have a fixed structure, like first half of columns are letters, and the next one - the corresponding columns of their scores:

half = len(df.columns)//2
score = df.iloc[:, half:]

category_level = np.add(
    score <= 10,
    score <= 20,
    dtype=int     # need this to accumulate integers, not booleans
)

category_formatting = [   
    'background-color: blue',          # default color
    'background-color: lightgreen',    # <=10
    'background-color: yellow',        # <=20
]

formatting = np.choose(category_level, category_formatting)

At this point, formatting is a DataFrame with column names from the second half. To get the right applying, we have to replace column names with their twins from the first half:

formatting.columns = df.columns[:half]
styled_df = df.style.apply(lambda _: formatting, axis=None)