"Dino was never very sociable, but he is really important to me. I was so relieved when my neighbours said they'd spotted him, but now I'm really worried he will die.
"He escaped three weeks ago when it was really warm weather, but now it's getting colder and he hasn't eaten for three weeks.
"I can see him from my back garden and he is just clinging on to the end of a branch. I hope he is strong enough to hold on because the wind is picking up."
The iguana, estimated to weigh about 22lb (10kg), was spotted by 27-year-old beautician Leanne Verdin and her cousin, Gaynor Taylor, 32, up a tree in the garden of 55-year-old retired tannery worker George Harris.
His property, on Woolton Lane, backs on to Miss Owen's next door neighbour.
Mr Harris called the fire brigade, who attended with the RSPCA since they are not trained to deal with "vicious animals".
Ann Grain, spokeswoman for the RSPCA, said: "The iguana was about 50ft up the tree, too high for our officers to climb up. The decision was made to leave it there.
"Iguanas are tree dwelling animals and it will come down eventually when it is hungry. Our officer has told the owner to keep an eye on it and, when it does start to climb down, to call us immediately and we will come out and get it down."