I have a borrower who is refinancing a single unit investment property.

Cash out - It is not purchase money, it is not improvement money.

Does TRID apply? Do I issue an LE / CD or do I use something else?

Define investment property and what he is using the cash out for. Is he a professional real estate investor? TRID is purpose driven not collateral driven.

Condo
Cash out to pay off another investment property

I don't think it applies - the purpose is business related.
He is not a "professional real estate investor"
Has a job - owns a few investment properties

Rent homes? Or flip homes? (I hate the term "investment property"...just saying. Could be consumer investment or business....that term doesn't tell you enough.)

Regulation Z addresses two type of loans, consumer purpose and business purpose. The word "investment" is not used in Regulation Z. Business purpose loans are exempt from Regulation Z.

Investment can mean a variety of things. A loan that is for investment, would have to be examined under the general business purpose test found in Regulation Z below.

Official Interpretation
3(a) Business, Commercial, Agricultural, or Organizational Credit

3. Factors. In determining whether credit to finance an acquisition—such as securities, antiques, or art—is primarily for business or commercial purposes (as opposed to a consumer purpose), the following factors should be considered:
i. General.
A. The relationship of the borrower's primary occupation to the acquisition. The more closely related, the more likely it is to be business purpose.
B. The degree to which the borrower will personally manage the acquisition. The more personal involvement there is, the more likely it is to be business purpose.
C. The ratio of income from the acquisition to the total income of the borrower. The higher the ratio, the more likely it is to be business purpose.
D. The size of the transaction. The larger the transaction, the more likely it is to be business purpose.
E. The borrower's statement of purpose for the loan.

As you can see – whether the investment was a piece of art or it was the purchase of real estate, there could be a difference on whether the loan was for a business purpose. If I buy a painting and call it an investment, unless I am in the art business, this would be a personal investment and not a business investment. The same would hold true for someone who had purchased other non-rental property, if they were not actively involved in the business of real estate.

Rental property
He doesn't live in it
It is not being rehabbed

Remove the word investment

Reg.Z specifically addresses rental property farther down in the commentary Randy quoted,
"
4. Non-owner-occupied rental property. Credit extended to acquire, improve, or maintain rental property (regardless of the number of housing units) that is not owner-occupied is deemed to be for business purposes. This includes, for example, the acquisition of a warehouse that will be leased or a single-family house that will be rented to another person to live in. If the owner expects to occupy the property for more than 14 days during the coming year, the property cannot be considered non-owner-occupied and this special rule will not apply. For example, a beach house that the owner will occupy for a month in the coming summer and rent out the rest of the year is owner occupied and is not governed by this special rule. ( See comment 3(a)–5, however, for rules relating to owner-occupied rental property.)"

As you can see the applicability still relates to the purpose of the funds, not the collateral. I would argue that funds to payoff another non-owner occupied rental property would be to "maintain" the property and treat as business purpose and therefore Reg.Z/TRID does not apply.

So could one argue that an individual who happens to have 3 non-owner occupied rental properties, and is requesting a refinance of a rental property would be requesting a business-purpose loan?

How to treat transactions involving rental property whether if they have one or 100 is clearly defined. The OP was talking about "investment" property, which is not.

Ah, I didn't catch on to that part.