She found her lost dog quite by chance

The answer is NO.
You can say the following:
She found her lost dog only by chance.-- OK
She found her lost dog purely by chance.-- OK
She found her lost dog absolutely by chance.-- OK
She found her lost dog all by chance.-- Wrong
Hope this helps.
Cheers
Note:本人已在海外生活了数十载.为了慎重起见,我的答案都与老美或老英交换过意见,你放心使用吧.如有任何问题,可补而述之.

可以