If you have SLE, your rheumatologist should be monitoring all of your medications. Anticoagulants are prescribed for a variety of reasons and, while they should not interfere or exacerbate reflux, it's a good idea to discuss this with both the prescribing physician as well as any specialists you see. The pharmacy should be monitoring your drug combinations as well.
If you are taking anticoagulants and are receiving medication for acid reflux, it would be best to speak to your doctor. The medications can interact causing an increase in the effect of the anticoagulant. As far as having lupus, I saw no specific references stating you should not take an anticoagulant due to having this autoimmune disease.
The reactions of Lupus with medication are different for different people. In general no, you can not take an anticoagulant with Lupus, however you would need to discuss any type of medication you are thinking of taking with your doctor. Your coctor is the one who will be more aware of what your condition is and your meds.