The radio DJ was taken to hospital on Friday just hours after she attended two different public functions.
A source told The Sun: "It all happened very quickly. Lisa started to feel poorly when she turned on the Bond Street Christmas lights in London.
"She hosted an awards ceremony later and began to feel really peaky. She was feeling so weak when she arrived at the hospital she was on the verge of collapse."
A friend also told the Daily Mail: "Lisa was feeling rotten for a good few days. She had flu symptoms, major aches and pains and a migraine."
Snowdon - who presents Capital Radio's breakfast show with Johnny Vaughan - has not yet been discharged from hospital but is believed to be on the road to recovery.
"Lisa's unlikely to be returning to the breakfast show next week," the friend added. "She is now on the mend, but she's still in hospital. The doctors have warned her this takes a long while to recover from."
Saturdays singer Frankie Sandford is currently standing in for Snowdon on her morning radio show.
