OK, moving this from a comment to an answer.
Note about "tenses" in Biblical Hebrew. Technically speaking the idea of "zman 'avar"/'past tense' is Modern Hebrew. In Biblical Hebrew, you have aspects rather than tenses: perfect/imperfect. So [lo] halakh is in what's called the simple perfect[ive] aspect. The verbal system in Biblical Hebrew is somewhat different than Modern (as well as European languages like English). Perfect verbs generally indicate that the action or concept is whole or complete, which is usually (but not always) an indication that they happened in the past — or the past up until the present.
Now there is a form that be used to indicate the "present" more clearly: a present participle (in this case, holekh). Literally, *ashrei ha'ish asher lo holekh means "Happy is the one who [is] not walking". However, Classical Biblical Hebrew tends to avoid the use of the participle as a "present tense" verb — while it does use the present participle as a substantive (noun), an adjective, a relative, and a predicate, the use of the participle to represent the present tense is largely a feature of Late Biblical, and especially Mishnaic, Hebrew. As Waltke and O'Connor write: "the participle does not function in Biblical Hebrew as a finite verb with a distinct time reference, though such use is regular in Mishnaic and later Hebrew; thus the words yodea' ani would in Biblical Hebrew have the sense 'I am one who knows,' while in Mishnaic Hebrew they mean simply 'I know'".
So: in the context of Psalms, "lo halakh" could definitely be translated as a simple present, i.e. "does not walk", as well as "has not walked".
Kelly indicates that "a perfect may be translated in the present tense when it represents a verb of perception, attitude, disposition, or mental or physical state of being", and gives as examples Isaiah 59:8, I Samuel 8:5, and Malachi 1:2. Similarly, Waltke and O'Conner write that "sometimes the perfective conjugation is used for present-time situations. This combination creates creates notional tensions because the form entails a single aspect, but present time tends to entail imprefective aspect... Hebrew may use its perfective form with the same, present/habitual significance ("the gnomic perfective") [example: Jeremiah 8:7]. Hebrew also uses its perfective form for a present situation in which a speaker resolves on a future action."
The "gnomic perfective" is the kind of form used when expressing things that happen all the time, i.e. in proverbs and sayings. So here it's not talking about one specific person who is currently walking, but rather the idea of a person who walks.