entity_id   lat   lon   time

1001        34.5  14.2  4:55 pm
1001        34.7  14.5  4:58 pm
1001        35.0  14.6  5.03 pm

1002        27.1  19.2  2:01 pm
1002        27.4  19.3  2:08 pm
1002        27.4  19.9  2:09 pm

import pandas as pd
import numpy as np
from geopandas import GeoDataFrame
from shapely.geometry import Point, LineString

# Zip the coordinates into a point object and convert to a GeoDataFrame
geometry = [Point(xy) for xy in zip(df.lon, df.lat)]
df = GeoDataFrame(df, geometry=geometry)

# Aggregate these points with the GroupBy
df = df.groupby(['entity_id'])['geometry'].apply(lambda x: LineString(x.tolist()) if x.size > 1 else x.tolist())
df = GeoDataFrame(df, geometry='geometry')

df = df.groupby(['entity_id'])['geometry'].apply(lambda x: LineString(x.tolist()) if x.size > 1 else x.tolist())