Is there a canonical example of when ridge outperforms lasso? Can someone please give me an example of when ridge would out perform lasso? 
Won't lasso do better in most circumstances? If a regressor has a large coefficient, that means the regressor is a good predictor, so if we use ridge, we penalize that coefficient more. Isn't that bad?? Lasso will penalize the smaller coefficients more and the larger coefficients less because ridge squares the coefficient in the loss function (L2 norm), while lasso is just L1 norm. 
We want less coefficients to prevent over-fitting, so wouldn't lasso ALWAYS be better? 
Lasso will obviously be better if there are 2 good regressors and 15 bad ones, is there a canonical example of when ridge would outperform lasso? 
 A: Both models penalise the inclusion of a non-zero coefficient, using a penalty function.  LASSO regression penalises in a way that is proportionate to the absolute magnitude of the coefficient, and ridge regression penalises in a way that is proportionate to the square of the coefficient.  Neither model penalises inputs in the likelihood function where the coefficient is set to zero.  For inputs into the likelihood function where a coefficient is non-zero, LASSO regression penalises values near zero more heavily, whereas ridge regression penalises values far from zero more heavily.  (In your question, you seem to be making the error of thinking that the squared value is always more than the absolute value.  That is not true.  For input values with magnitude less than one, the absolute value is larger than the square.)
Intuition tells us that ridge regression will tend to outperform LASSO regression in cases where the true non-zero coefficients are close to zero, relative to the noise in the regression.  In this case, ridge regression penalises these values less, so it is more likely to estimate non-zero values for these coefficients.  LASSO regression penalises these coefficients more, so it is more likely to incorrectly estimate them to be zero.  On the basis of this intuition, I would recommend that you compare these models for some data generated from a regression with coefficients that are small relative to the noise in the regression.  If you were to conduct a simulation study with cases like this, you should find that ridge regression tends to outperform LASSO in these cases.
A: Ridge was originally designed for correlated variables, and that's where it's best.
Consider examinations to determine a degree. ( Which supposedly is measuring ability)
Which do you think is more reliable: taking the average of all the exams or picking a single exam most correlated with ability (if there is one)? Averaging over the different exams removes (independent noise - you didn't sleep well one day etc)
Ridge will take the average of these correlated inputs (IE the separate exams), whilst lasso will just select one.
