diff --git a/Library/Homebrew/rubocops/cask/no_overrides.rb b/Library/Homebrew/rubocops/cask/no_overrides.rb
index 82d8740d67..deb632724c 100644
--- a/Library/Homebrew/rubocops/cask/no_overrides.rb
+++ b/Library/Homebrew/rubocops/cask/no_overrides.rb
@@ -40,6 +40,10 @@ module RuboCop
 
             node.child_nodes.each do |child|
               child.each_node(:send) do |send_node|
+                # Skip (nested) livecheck blocks as its `url` is different to a download `url`.
+                next if send_node.method_name == :livecheck
+                next if send_node.parent.block_type? && send_node.parent.method_name == :livecheck
+
                 # Skip string interpolations (`:begin` inside `:dstr`).
                 next if send_node.begin_type? && send_node.parent_node.dstr_type?
                 next if ON_SYSTEM_METHODS.include?(send_node.method_name)
diff --git a/Library/Homebrew/test/rubocops/cask/no_overrides_spec.rb b/Library/Homebrew/test/rubocops/cask/no_overrides_spec.rb
index cd1dc3c436..60d7263d59 100644
--- a/Library/Homebrew/test/rubocops/cask/no_overrides_spec.rb
+++ b/Library/Homebrew/test/rubocops/cask/no_overrides_spec.rb
@@ -38,6 +38,29 @@ describe RuboCop::Cop::Cask::NoOverrides do
     include_examples "does not report any offenses"
   end
 
+  context "when there are livecheck blocks within `on_*` blocks, ignore their contents" do
+    let(:source) do
+      <<~CASK
+        cask 'foo' do
+          on_intel do
+            livecheck do
+              url 'https://brew.sh/foo' # Livecheck should be allowed since it's a different "kind" of URL.
+            end
+            version '1.2.3'
+          end
+
+          on_arm do
+            version '2.3.4'
+          end
+
+          url 'https://brew.sh/foo.pkg'
+        end
+      CASK
+    end
+
+    include_examples "does not report any offenses"
+  end
+
   context "when there's only one difference between the `on_*` blocks" do
     let(:source) do
       <<~CASK