Exhibit 99.(g)(v)

LETTER AMENDMENT

December 13, 2021

State Street Bank and Trust Company

1200 Crown Colony Drive, JQB5S

Quincy, MA 02169

Attn: Suzanne Hinckley, Managing Director

Dear Sir or Madam:

Lord Abbett & Co. LLC (“Lord Abbett”), as a party to the Custodian and Investment Accounting Agreement between various Lord Abbett-sponsored investment companies and State Street Bank and Trust Company (“State Street”) dated November 1, 2001, as amended (the “Agreement”), requests an amendment to the Agreement pursuant to Section 17.

Section 17 of the Agreement provides that: “in the event that a Fund establishes one or more series with respect to which it desires to have State Street render services as custodian and recordkeeper under the terms of the Agreement, it shall so notify State Street in writing, and if State Street agrees in writing to provide such services, such series of Shares shall become a Portfolio under the terms of the Agreement.” This Letter Amendment is to notify State Street that on September 28, 2021, the Board of Directors of Lord Abbett Municipal Income Fund, Inc. (the “Company”) approved the filing of the Articles Supplementary to add Lord Abbett Sustainable Municipal Bond Fund, a series of the Company, (the “Portfolio”). It is the Company’s desire to have State Street render services as custodian and recordkeeper to the Portfolio under the terms of the Agreement; therefore, the Company requests that State Street agree, in writing, to provide such services to the Portfolio, thereby making the Portfolio a Portfolio under the terms of the Agreement.

Attached is an Amended Exhibit A to the Agreement that includes the name of the Fund as an entity that participates in the Agreement effective with the Fund’s commencement of operations (currently anticipated to be in January 2022).

Accordingly, we appreciate your prompt attention to this matter. Please indicate State Street’s acceptance by signing below.

Accepted:

/s/ Suzanne M. Hinckley

Suzanne M. Hinckley, Senior Vice President

State Street Bank and Trust Company

Date:

Enclosure

EXHIBIT A

Amended as of September 28, 2021¹

(Effective as of January 2022)

¹   As amended on September 28, 2021 to reflect the addition of Lord Abbett Sustainable Municipal Bond Fund, a series of Lord Abbett Municipal Income Fund, Inc.

²   Effective November 1, 2021, Lord Abbett High Yield Municipal Bond Fund and Lord Abbett Short Duration High Yield Municipal Bond Fund were renamed Lord Abbett High Income Municipal Bond Fund and Lord Abbett Short Duration High Income Municipal Bond Fund, respectively.