I am interested in problems of the form $$ u_t = F(u) + S(u) $$ where $F(u) = - div(f(u))$ and $S(u)$ is a stiff source term. I am looking for any existing works which develop Lax-Wendroff type schemes for such stiff problems using an IMEX approach to deal with stiff source. So far my search has yielded nothing more than Crank-Nicholson for the source  which is not good for stiff case. Is there any fundamental difficulty in constructing Lax-Wendroff schemes which are L-stable ?
The LW schemes I am looking at are of the form as used in . Perhaps LW is not a good name, they seem to be called two-derivative schemes. At second order, they are basically an LW scheme.
 Yuangao Zhang and Behrouz Tabarrok, Modifications to the Lax–Wendroff scheme for hyperbolic systems with source terms, https://doi.org/10.1002/(SICI)1097-0207(19990110)44:1%3C27::AID-NME485%3E3.0.CO;2-0
 Christlieb et al., Explicit Strong Stability Preserving Multistage Two-Derivative Time-Stepping Schemes, DOI: 10.1007/s10915-016-0164-2