I would like to ask given its close proximity to Taipei Main Station, is there lift/elevator that connected the hotel lobby to the basement of the station?
yes, it has the lift to hotel.
There is a lift from the hotel that connects to the basement of the hotel. There are some eateries and shops at this basement. It also leads directly into the station, but there is a small flight of steps that you need to take. So if you have luggage, you do have to lug them up that small flight of steps.
Get an answer from Caesar Park Taipei staff and past guests.