In a breach of non-compete or non-solicit lawsuit, the former employer will almost always claim their customer lists are trade secrets.  Texas Courts consider the following factors when determining if something is a  trade secret:

(1) the extent to which the information is known outside of his business; (2) the extent to which it is known by employees and others involved in his business; (3) the extent of the measures taken by him to guard the secrecy of the information; (4) the value of the information to him and to his competitors; (5) the amount of effort or money expended by him in developing the information; and (6) the ease or difficulty with which the information could be properly acquired or duplicated by others.

Texas Courts have found that customer lists can be trade secrets:

The Texas Supreme Court has noted that merely because a trade secret can be discovered by fair and lawful means does not preclude its owner of the right to protection from those who would secure possession of it by unfair means. See K & G Oil Tool & Serv. Co. v. G & G Fishing Tool Serv.,  314 S.W.2d 782, 788 (1958). This general rule applies to customer lists. See American Precision Vibrator Co., 764 S.W.2d at 278. Therefore, although a customer list may be considered a trade secret, to be entitled to the protection of the court, the proprietary information must be more than merely of a kind and character encompassed by the definition. The information must not be publicly available or readily ascertainable by independent investigation. (citations omitted)  A corollary to this is when a customer list is not considered to be a trade secret and its contents are readily ascertainable from sources other than the employer’s records, the former employee may legitimately compete with his former employer for those customers. 

Adco Indus. v. Metro Label Corp., 2000 Tex. App. LEXIS 5644 (Tex. App. Dallas Aug. 23, 2000).

An employer claiming a customer list is a trade secret must treat it as such.  Lists should not be "floating" around the office and should be protected via a computer password or some other type of precaution.  The employer should also be a able to document and demonstrate the origins of the list (i.e. developed over many years) and should identify it at as a trade secret in any non-compete, non-disclosure, or non-solicit agreement.  This will not guarantee trade secret protection but is a good start.