Envelope Theorem in Keen and Slemrod (2017)
At first glance, it appears the answer should be $\frac{dW}{dt}= -(z + tz_t) + v'*(z + tz_t)$, as $l$ and $e$ are chosen optimally and the envelope theorem cancels these terms out. Furthermore, one could expect both $z_t$ terms in the final derivative to drop out due to the envelope theorem. However, one and only one $z_t$ term remains in the authors' calculations.

The envelope theorem is just an application of first order conditions. In this case, it is better to simply use the first order conditions we know to derive the results, instead of using the theorem directly. I believe the authors invoke the term "envelope property" to concisely convey that they are using the previously found first order conditions. 

Taking the total derivative we arrive at: 

$\frac{dW}{dt}= wl_t -z - tz_t -c_ee' - \psi'l_t + v'*(z + tz_t)$

Inserting the expression for $z_t$ and grouping some terms we have:

$\frac{dW}{dt}= l_t[w(1-t)-\psi'] + e'[t-c_e] - z + v'*(z + tz_t)$

Note that the terms in square brackets are the same as the first order conditions for $l$ and $e$ and hence equal to zero. This leaves us with:

$\frac{dW}{dt}= - z + v'*(z + tz_t)$