If you want to do something to the input before predicting or something to the output before it gets used to update the target (and thus the next features that rely on lags), you can pass a function to run at any of these times. Here are a couple of examples: 
import copy

import lightgbm as lgb
import numpy as np
from IPython.display import display

from mlforecast import MLForecast
from mlforecast.utils import generate_daily_series

series = generate_daily_series(1)

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Before predicting

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Inspecting the input

We can define a function that displays our input dataframe before predicting. 
def inspect_input(new_x):
    """Displays the model inputs to inspect them"""
    display(new_x)
    return new_x
And now we can pass this function to the before_predict_callback argument of MLForecast.predict. 
fcst = MLForecast(lgb.LGBMRegressor(verbosity=-1), freq='D', lags=[1, 2])
fcst.fit(series, static_features=['unique_id'])
preds = fcst.predict(2, before_predict_callback=inspect_input)
preds
unique_idlag1lag2
0id_04.155933.000028
unique_idlag1lag2
0id_05.2502054.15593
unique_iddsLGBMRegressor
0id_02000-08-105.250205
1id_02000-08-116.241739

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Saving the input features

Saving the features that are sent as input to the model in each timestamp can be helpful, for example to estimate SHAP values. This can be easily achieved with the SaveFeatures callback. 
from mlforecast.callbacks import SaveFeatures

fcst = MLForecast(lgb.LGBMRegressor(verbosity=-1), freq='D', lags=[1])
fcst.fit(series, static_features=['unique_id'])
save_features_cbk = SaveFeatures()
fcst.predict(2, before_predict_callback=save_features_cbk);
Once we’ve called predict we can just retrieve the features. 
save_features_cbk.get_features()
unique_idlag1
0id_04.155930
1id_05.281643

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After predicting

When predicting with the recursive strategy (the default) the predictions for each timestamp are used to update the target and recompute the features. If you want to do something to these predictions before that happens you can use the after_predict_callback argument of MLForecast.predict.

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Increasing predictions values

Suppose we know that our model always underestimates and we want to prevent that from happening by making our predictions 10% higher. We can achieve that with the following: 
def increase_predictions(predictions):
    """Increases all predictions by 10%"""
    return 1.1 * predictions

fcst = MLForecast(
    {'model': lgb.LGBMRegressor(verbosity=-1)},
    freq='D',
    date_features=['dayofweek'],
)
fcst.fit(series)
original_preds = fcst.predict(2)
scaled_preds = fcst.predict(2, after_predict_callback=increase_predictions)
np.testing.assert_array_less(
    original_preds['model'].values,
    scaled_preds['model'].values,
)