To find a hamster that has run away and is lost in the house, you can try the following methods:
Close all exits: Once you find that the hamster has escaped from its cage, immediately close all the doors, windows, and small openings that allow the hamster to get out. This prevents the hamster from entering other rooms or running outside.

Food luring method: Place the hamster's favorite foods such as sunflower seeds, nuts, small cookies, etc. in different places and wait for the hamster to be attracted out by the food. You can put the food in the corners of the room or the places where the hamster often appears. Observe which places the food has been touched to determine the hamster's activity range.
Locating by sound method: Put some plastic bags or cardboard in the places where you think the hamster might go. When the hamster steps on these items, it will make a sound, which helps to determine its position.
Searching at night: Hamsters are nocturnal animals and are more active at night. You can keep quiet at night and gently shine a flashlight on every corner of the room to check if there is a hamster.
Setting a trap: You can make a simple trap. For example, make a simple trap using a small bucket and a handkerchief, or use a professional mouse trap to lure and catch the hamster.
Using smell: Place the hamster's cage, toys, bedding materials, etc. in various corners of the room. Hamsters are very sensitive to their own smell, and these items will attract it out.
Carpet search: Carefully check each room, and focus on searching under furniture such as sofas, beds, and cabinets, as well as in dark corners like the corners of the walls.
Be patient and keep quiet: Try to keep quiet during the search process to avoid making noises that might scare the hamster. Search patiently and don't be too hasty.