There's a lot to consider. For a lead generation deal to be fair to both parties though, a fee for *qualified* leads needs to be in place whether the lead converts or not. Notice there's a big distinction between "qualified" and "quality."
If someone sends you 50 *qualified* leads and you only convert 1 or less, the problem might be with the conversion part and the lead producer shouldn't be held responsible for that.
What you should do is test out 2 or 3 lead generation methods. 1 of them being the other speech pathologist, measure out the conversion rates and then establish a base price. Then monitor the quality of the leads. 45-90 days is a good time-frame to make judgments, comparisons and adjustments.
But what is not equitable to the referring party is to say I will only pay you if your lead converts, because without knowing all the components of the process, the same leads that didn't convert with you might convert really well for a competing business.
A fixed price with a bonus structure would be good to make sure the receiving party is going a good job at actually converting the lead and for the referring party to be incentivized to send leads.