diff --git a/cmake/Modules/Packages/KIM.cmake b/cmake/Modules/Packages/KIM.cmake
index 84d9ec9c71..c1e52bd3e5 100644
--- a/cmake/Modules/Packages/KIM.cmake
+++ b/cmake/Modules/Packages/KIM.cmake
@@ -35,6 +35,8 @@ if(PKG_KIM)
   option(DOWNLOAD_KIM "Download KIM-API from OpenKIM instead of using an already installed one" ${DOWNLOAD_KIM_DEFAULT})
   if(DOWNLOAD_KIM)
     message(STATUS "KIM-API download requested - we will build our own")
+    # Workaround for cross compilation with MinGW, which messes up ${CMAKE_INSTALL_LIBDIR}
+    string(REPLACE ${CMAKE_INSTALL_PREFIX} "" _KIM_LIBDIR ${CMAKE_INSTALL_LIBDIR})
     include(ExternalProject)
     enable_language(C)
     enable_language(Fortran)
@@ -50,11 +52,11 @@ if(PKG_KIM)
                  -DCMAKE_BUILD_TYPE=${CMAKE_BUILD_TYPE}
                  -DCMAKE_MAKE_PROGRAM=${CMAKE_MAKE_PROGRAM}
                  -DCMAKE_TOOLCHAIN_FILE=${CMAKE_TOOLCHAIN_FILE}
-      BUILD_BYPRODUCTS <INSTALL_DIR>/${CMAKE_INSTALL_LIBDIR}/libkim-api${CMAKE_SHARED_LIBRARY_SUFFIX} 
+                 BUILD_BYPRODUCTS <INSTALL_DIR>/${_KIM_LIBDIR}/libkim-api${CMAKE_SHARED_LIBRARY_SUFFIX} 
       )
     ExternalProject_get_property(kim_build INSTALL_DIR)
     set(KIM-API_INCLUDE_DIRS ${INSTALL_DIR}/include/kim-api)
-    set(KIM-API_LDFLAGS ${INSTALL_DIR}/${CMAKE_INSTALL_LIBDIR}/libkim-api${CMAKE_SHARED_LIBRARY_SUFFIX})
+    set(KIM-API_LDFLAGS ${INSTALL_DIR}/${_KIM_LIBDIR}/libkim-api${CMAKE_SHARED_LIBRARY_SUFFIX})
     list(APPEND LAMMPS_DEPS kim_build)
   else()
     find_package(KIM-API ${KIM-API_MIN_VERSION} REQUIRED)
diff --git a/cmake/Modules/Packages/LATTE.cmake b/cmake/Modules/Packages/LATTE.cmake
index bc89b00111..093c9b7f22 100644
--- a/cmake/Modules/Packages/LATTE.cmake
+++ b/cmake/Modules/Packages/LATTE.cmake
@@ -9,6 +9,8 @@ if(PKG_LATTE)
   option(DOWNLOAD_LATTE "Download the LATTE library instead of using an already installed one" ${DOWNLOAD_LATTE_DEFAULT})
   if(DOWNLOAD_LATTE)
     message(STATUS "LATTE download requested - we will build our own")
+    # Workaround for cross compilation with MinGW, which messes up ${CMAKE_INSTALL_LIBDIR}
+    string(REPLACE ${CMAKE_INSTALL_PREFIX} "" _LATTE_LIBDIR ${CMAKE_INSTALL_LIBDIR})
     include(ExternalProject)
     ExternalProject_Add(latte_build
       URL https://github.com/lanl/LATTE/archive/v1.2.1.tar.gz
@@ -18,17 +20,20 @@ if(PKG_LATTE)
       -DBLAS_LIBRARIES=${BLAS_LIBRARIES} -DLAPACK_LIBRARIES=${LAPACK_LIBRARIES}
       -DCMAKE_Fortran_COMPILER=${CMAKE_Fortran_COMPILER} -DCMAKE_Fortran_FLAGS=${CMAKE_Fortran_FLAGS}
       -DCMAKE_Fortran_FLAGS_${BTYPE}=${CMAKE_Fortran_FLAGS_${BTYPE}} -DCMAKE_BUILD_TYPE=${CMAKE_BUILD_TYPE}
-      -DCMAKE_MAKE_PROGRAM=${CMAKE_MAKE_PROGRAM}
-      BUILD_BYPRODUCTS <INSTALL_DIR>/${CMAKE_INSTALL_LIBDIR}/liblatte.a
+      -DCMAKE_MAKE_PROGRAM=${CMAKE_MAKE_PROGRAM} -DCMAKE_TOOLCHAIN_FILE=${CMAKE_TOOLCHAIN_FILE}
+      BUILD_BYPRODUCTS <INSTALL_DIR>/${_LATTE_LIBDIR}/liblatte.a
     )
-    ExternalProject_get_property(latte_build INSTALL_DIR)
-    set(LATTE_LIBRARIES ${INSTALL_DIR}/${CMAKE_INSTALL_LIBDIR}/liblatte.a)
     list(APPEND LAMMPS_DEPS latte_build)
+    ExternalProject_get_property(latte_build INSTALL_DIR)
+    set(LATTE_LIBRARIES ${INSTALL_DIR}/${_LATTE_LIBDIR}/liblatte.a)
   else()
     find_package(LATTE)
     if(NOT LATTE_FOUND)
       message(FATAL_ERROR "LATTE library not found, help CMake to find it by setting LATTE_LIBRARY, or set DOWNLOAD_LATTE=ON to download it")
     endif()
   endif()
+  if(NOT LAPACK_FOUND)
+    add_dependencies(latte_build linalg)
+  endif()
   list(APPEND LAMMPS_LINK_LIBS ${LATTE_LIBRARIES} ${LAPACK_LIBRARIES})
 endif()