I just watched this and I can definitely see what you are saying. We see Jacoby with Ben in his office in one scene and almost literally in the next scene Jacoby is with Lana and claims they've been together for "almost the past 24 hours". There does seem to be some inconsistency or possible mixup of details here and its possible this was simply an overlooked detail.
That said I do have a possible interpretation based on what can be evidenced from the episode. In the scene in Ben's office, Ben says:
Jeb, there is a great day upon us. By dawn, our troops wiII be on the outskirts of Washington. By midday, it wiII faII.
At the end of the scene when Ben and Jacoby are singing Dixie, we see an outside shot of The Great Northern at what appears to be dusk.
The very next scene is Major Briggs stumbling into the sheriff's office on what is definitely a different time of day if not a completely new day as there is plenty of light outside. And minutes later we see the part where Jacoby claims to have been with Lana for almost 24 hours.
To me all of these facts seem to indicate that the scene with Ben occurred at the end of one day and the scene with Lana occurred on a subsequent day and while we are seeing the scenes only minutes apart, at least a half day or so has gone by. Of course a half a day isn't 24 hours, but I wouldn't put it past Dr Jacoby to spend 12 hours with someone and then call that "almost 24 hours".
One should also consider the fact that Lana clearly has the ability to put a spell on any man that she spends only a few minutes with to get them to do anything for her as is demonstrated by her spending less than a minute with the mayor and changing his mind from wanting to shoot her to wanting to adopt a child with her.