Cressy is a one-year-old brown cross with half a front leg and was found abandoned as a tiny puppy.
She was rescued from Romania by Lesa Valentine.
Lesa, who lives on Clarendon Road in Morecambe, has eight rescue dogs and works to give dogs a new home.
Lesa had only just bought the stroller for £85 when it was stolen from her front garden on Saturday.
She said: “I just want it back. I don’t think the person, whoever took it, understands how much we need it and how much Cressy needs it.
“Now we will have to put her in the van and drive down to the beach which is just not the same. It has put an end to our Saturday morning walks.”
The stroller is usually covered in Lesa’s front garden but on Saturday night Lesa says the cover must have blown off as it was no longer there the next day.
Lesa has been overwhelmed by the response she has received on social media.
A friend has set up a fundraising page to help Lesa replace the stolen stroller, visit www.gofundme.com/2r2yu9g