This is an interesting question. The brewing reactions take place quite slowly so that one is never at equilibrium. This casts some doubt as to when the reading which we declare to represent the mash pH should be taken. When I first poo-pooed the notion of software prediction of mash pH I would often ask the question of those who assayed to make such predictions what epoch was to be assigned to their estimates. When I started exploring this subject in detail and realized that the key to mash pH prediction, were it possible, would rely on malt titration curves and started collecting malt titration data it was apparent that the question of when was an important one. If one has added acid or base to his mash water or grist the pH meter at first exposure to the mash measures the pH of the liquid in the mash tun which is pretty much the mash liquor as the grist particles haven't solubilized yet. Thus early readings on a mash to which acid has been added (as in OP here) are going to be low (as OP indicates they were). The opposite will be observed in cases where base has been added to the liquor or grist. In either case the liquid starts to penetrate the grain, starch granules burst and the mashing reactions begin. While this is going on mash pH begins to move towards equilibrium and a trace of mash pH over time exhibits typical assymptotic behaviour. After 25 to 30 minutes the rate of change of pH will have slowed but as is the case with OP will continue to rise or fall gradually over however long the mashing process continues. Thus a good brewer will, with a new beer at least, monitor pH many times starting at strike and ending when the beer is in the package. This pH history serves as a set of mileposts along the way. The brewer knows where pH should be half an hour after strike, at the time he returns the second decoction, as he goes into the kettle, 24 hours after pitching and so on. A deviation at any of these points is a signal to him that something isn't right (though, of course, variances in malts will lead to some deviations but he knows, with experiences, how large those deviations can be without causing alarm).
If we are going to attempt mash pH prediction properly we have to have malt titration data and the titration curve for a given malt depends rather sharply on whether the pH values that go into the titration curve were measured at 5 minutes or 10 minutes. The differences between titration curves measured at 25 minutes and 30 minutes are going to be much smaller but they will not be the same, in some cases, as a titration curve measured at an hour. At the same time we recognize that most of the character of the beer has been determined by 30 minutes. The reason we mash longer is to squeeze that last bit of fermentable out of the grain. With decoction mashing we only mash longer because the rest mash has to do something while the decoction is processing. Given this, and given that collection of a complete set of titration curves out to an hour is terribly impractical (it takes quote a bit of work to get a titration curve) it seems reasonable to pick 25 min or half an hour. If our measured pH at half an hour is a fair representation of what we predicted using half hour titration data then we know, fairly early on, that we didn't make some mistake like bobbling a kg to pounds conversion or slipping a decimal point in the water's alkalinity number. This is why I have always, and continue, to advocate half an hour as the number to use. Were pH prediction to be taken seriously, to the point that ASBC or EBC published methods for it, they would have to pick some number. Half an hour is, of course, arbitrary but I am guessing based on the way things work, that they would choose a number like this.
OP: The rapid rise in pH you observed is quite normal given that you used lactic acid. Creep upwards past half an hour is also normal but in this case seems a bit high. It is probably worth doing a stability check on your electrode. As your electrode is getting on in years it is also probably worth checking its step response. Let it stabilize completely (or as completely as it will) in 4 buffer then rinse it off quickly with DI water, shake or blot it dry and then pop it into pH 4 buffer. See how long it takes to stabilize at 4.
