An outdoor table lamp is the lounge side lamp, moved out to the patio. Same job, same 300 to 600 lumens at eye level when seated. What changes is the IP rating, the cable and how it copes with wind.
IP44 under a canopy, IP65 in the rain, and back indoors for winter
The choice is small. A round head on a slim stem, a 32 cm disc and an anthracite cone make up the whole section for now. IP44 is enough under a canopy or a covered pergola. Out in the rain, IP65. Over winter, it comes indoors with the cushions.
The cable, 1.50 m on one model, and the socket at the end of it
Measure the distance to the socket first. A 1.50 m cable needs a socket within reach, or an extension lead rated for outdoor use with a weatherproof connector. The socket must be on a circuit protected by a 30 mA RCD. If you're unsure, ask an electrician to check. None is sold as rechargeable or solar.
A heavy base, with the light aimed down
A 32 cm disc or a cone catches the wind like a sail. A weighted base and a modest height, below eye level when seated, stop it blowing over at the first gust of the evening; the weight is listed on the product page. Allow 300 to 600 lumens of warm white (2,700 to 3,000 K), with the source hidden or pointing down. At eye level, a bare bulb dazzles everyone round the table.
We'd advise against carrying the lounge lamp outside "just for tonight" on an indoor extension lead. For the patio itself, consider a garden wall light of 400 to 800 lumens on the house wall or a garden bollard of 200 to 500 lumens by the steps, while our guide to light fittings for your terrace shows how to combine all three around a seating area; the whole family is under outdoor lighting.
