diff --git a/conda-store-server/conda_store_server/action/generate_lockfile.py b/conda-store-server/conda_store_server/action/generate_lockfile.py
index 2fa2c327a..caf2d9118 100644
--- a/conda-store-server/conda_store_server/action/generate_lockfile.py
+++ b/conda-store-server/conda_store_server/action/generate_lockfile.py
@@ -37,6 +37,18 @@ def print_cmd(cmd):
     print_cmd(["conda", "config", "--show"])
     print_cmd(["conda", "config", "--show-sources"])
 
+    # conda-lock ignores variables defined in the specification, so this code
+    # gets the value of CONDA_OVERRIDE_CUDA and passes it to conda-lock via
+    # the with_cuda parameter, see:
+    # https://github.com/conda-incubator/conda-store/issues/719
+    # https://docs.conda.io/projects/conda/en/latest/user-guide/tasks/manage-virtual.html#overriding-detected-packages
+    # TODO: Support all variables once upstream fixes are made to conda-lock,
+    # see the discussion in issue 719.
+    if specification.variables is not None:
+        cuda_version = specification.variables.get("CONDA_OVERRIDE_CUDA")
+    else:
+        cuda_version = None
+
     # CONDA_FLAGS is used by conda-lock in conda_solver.solve_specs_for_arch
     try:
         conda_flags_name = "CONDA_FLAGS"
@@ -48,6 +60,7 @@ def print_cmd(cmd):
             platforms=platforms,
             lockfile_path=lockfile_filename,
             conda_exe=conda_command,
+            with_cuda=cuda_version,
         )
     finally:
         os.environ.pop(conda_flags_name, None)