Inclusion Criteria  Study participants meeting all of the following criteria will be allowed to enroll in the study:  Must be 55-90 years old, inclusive and have one of the following:  Subjective cognitive decline(SCD) Minor neurocognitive disorder(mild cognitive impairment(MCI)) Major neurocognitive disorder(possible or probable AD) OR  Must be 18-80 years old, inclusive and have one of the following:  Sporadic or familial ALS diagnosed as possible, laboratory-supported probable, probable, or definite as defined by the revised El Escorial criteria Asymptomatic carrier of an ALS-causative mutation per CLIA-certified genetic testing results (MGH site only)  Screening CSF level of  - CCL2 level ≥ 250 pg/mL  Up-to-date immunization records per CDC guidelines Must have received the Recombinant Zoster Vaccine (RZV, also known as Shingrix) within 4 years prior to enrollment. Note: Only one dose of RZV is needed prior to the Baseline Visit.  Must have received the COVID-19 vaccine prior to the Screening Visit with final dose received at least 14 days prior to the Screening Visit.  - It is strongly recommended that participants receive a COVID-19 booster vaccine before entering the trial if applicable per CDC/FDA guidelines. If the participant will be receiving a booster shot, it must received at least 14 days prior to the Screening visit.  For participants with ALS:  Must either not be taking riluzole or be on a stable dose of riluzole for at least 30 days prior to the Screening Visit. (Riluzole-naïve participants are permitted in the study.) Must either not be taking edaravone or be on a stable dose of edaravone for at least 1 cycle of infusions prior to the Screening Visit (Edaravone-naïve participants are permitted in the study.). ALSFRS-R score ≥ 27 Must be ambulatory, defined as able to walk at least within the home every day. Use of gait assistive devices is allowed. Some use of a wheelchair is also allowed. Greater than 12-month life expectancy in the opinion of the investigator  For participants with AD:  MoCA score ≥ 8 The participant must have a study partner that can accompany them to every visit and co-sign any informed consent document. Must either not be taking cholinesterase inhibitors or be on a stable dose of cholinesterase inhibitors for at least 3 months prior to the Baseline Visit (Cholinesterase inhibitor-naïve subjects are permitted in the study.). Ability to medically undergo LP in the opinion of the investigator (e.g., no bleeding disorder, allergy to local anesthetics, prior lumbar surgery which might make LP difficult, a skin infection at or near the LP site, evidence of high intracranial pressure, or anticipated difficulty getting into position for LP). Capable of providing informed consent and following study procedures. - In the case that a participant lacks the ability to provide informed consent, informed consent will be obtained from the participant's surrogate representative and assent obtained from the participant.  Exclusion Criteria  Study participants meeting any of the following criteria during screening evaluations will be excluded from entry into the study:  Women who are pregnant, breastfeeding, or planning to become pregnant during the trial Any unstable clinically significant medical condition other than ALS or AD (e.g., within six months of baseline, including but not limited to myocardial infarction, angina pectoris, congestive heart failure, or neoplasm undergoing active treatment). Active cancer or history of cancer, except for the following: basal cell carcinoma, cervical carcinoma in situ, prostatic carcinoma in situ, or other malignancies curatively treated and with no evidence of disease recurrence for at least 5 years. Active cancer includes cancers with current disease manifestations or therapy that could adversely affect participant safety and longevity, create the potential for drug-drug interactions, or compromise the interpretation of study results. History of diverticulitis or bowel perforation. Active, serious infection, including localized infection in the opinion of the investigator. Positive for latent or active tuberculosis (TB). Note: Patients with a history of latent or active TB must have had an adequate course of treatment documented prior to study participation. Evidence of active hepatitis B or C infection. History of severe hepatic or renal impairment. eGFR < 60 mL/min/1.73 m^2  Have any of the following specific abnormalities on screening laboratory tests:  ALT or AST >2.5x upper limits of normal (ULN) Alkaline phosphatase (ALP) ≥2x ULN Total bilirubin ≥1.5x ULN, Note: patients with elevated bilirubin secondary to Gilbert's disease are eligible to participate in the study. Hemoglobin <10 g/dL (100.0 g/L) Total white blood cell count <3000 cells/μL (<3.00 x 10^3/μL or <3.00 billion/L) Neutropenia (absolute neutrophil count [ANC] <1500 cells/μL) (<1.50 x 10^3/μL or <1.50 billion/L) Lymphopenia (lymphocyte count <1000 cells/μL) (<1.00 x 10^3/μL or <1.00 billion/L) Thrombocytopenia (platelets <100,000 cells/μL) (<100 x 10^3/μL or <100 billion/L) Laboratory abnormalities in vitamin B12, thyroid stimulating hormone (TSH), or other common laboratory parameters that might contribute to cognitive dysfunction Personal history of pulmonary embolus (provoked or unprovoked) or deep vein thrombosis, or a history of unprovoked pulmonary embolus in a first-degree family member. Treatment with anticoagulants that, in the opinion of the investigator, would compromise the safety of the participant. Previous therapy with baricitinib.  Current use of strong Organic Anion Transporter 3(OAT3) inhibitors (e.g., probenecid) or other prohibited medication (refer to Section 6.7.1) within 5.5 half-lives or 30 days of screening, whichever is longer.  - For participants with AD: Current use of Aducanumab or within 30 days of screening.  Receiving other experimental interventions for AD or ALS within 5.5 half-lives or 30 days of screening, whichever is longer. Use of permanent assisted ventilation (invasive ventilation via tracheostomy, or >22 hours of non-invasive ventilation per day, e.g., via BiPAP). Have had any major surgery within 8 weeks prior to screening or will require major surgery during the study that, in the opinion of the investigator, would pose an unacceptable risk to the patient. Note: Placement of a gastrostomy tube and an intravenous port are not considered major surgery.