I can't find anything that says you can't.
"While vitamin K foods promote blood clotting, you do not need to avoid any foods while taking Lovenox, according to Drugs.com.
Vitamin K and Anticoagulants
In the liver, your body uses vitamin K to produce the substances needed for blood clotting. Vitamin K interacts with certain anticoagulants, Coumadin and warfarin, decreasing their effectiveness in preventing your blood from clotting. When taking these specific anticoagulants, you need to eat a consistent amount of vitamin K each day to ensure your blood stays at the right consistency to prevent clotting. Because Lovenox does not interact with vitamin K, it is not necessary to limit or avoid foods high in vitamin K such as spinach, kale or broccoli."
MedlinePlus: Blood Thinners
Nutrition and Food Web Archive; Anticoagulants and Vitamin K; Christopher Theberge; 2007
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