In my opinion, you should take medicines that have helped you in the past. Depression may cause temporary cognitive impairment. Therefore, anything that helps cure depression helps cognition. Therefore, Lamictal may actually help in improving cognition. It is generally safe. If your doctor has suggested it, you should give it a trial. From your description of your mental state, I feel that you have significant depression and anxiety.
You will benefit from medicines.
Proper treatment of depressive episodes is shown to help reduce severity and treatment response of future episodes as well.
I hope this answer helps you.

Hi, thanks for the query; you are diagnosed with bipolar 1 which means you have had at least one episode of Mania & 1 or more episodes of depression. Simple answer is NO; lamotrigine (Lamictal) dosent cause cognitive deterioration. It causes dizziness, drowsiness, headache, blurred/double vision, loss of coordination, shaking (tremor), nausea, vomiting, or upset stomach with occasional worsening of depression & suicidal thoughts. Considering your symptom profile, you are most probably suffering from an episode of bipolar depression. Hence you need to Consult your GP/Psychiatrist for a detailed evaluation to ascertain its depression; followed by switch to either Lithium, Quetiapine, combination of Olanzapine+ Fluoxetine which are better drugs than lamotrigine in their own right as mood stabilizers. Lastly start doing 30 minutes daily physical exercise, try to sleep for at least 6-7 hours each night; stay away from alcohol & other illicit drugs. If required, get back to me for further assistance. Hope this helps; good luck