It was a fast day. Lavan was part of a group of seven people fasting, so wanted to pray mincha and read "Vay'chal". Of course, he started with "Ashre". (Later, Yaakov told him (per Mishna B'rura 566:14) that you need ten for "Vay'chal".)
Let's see why this was so, and how we see it from the p'sukim:
It was a fast day:
Let's work backwards from the next known date in the Chumash. In 33:16–17 we see Yaakov going to Sukos, where the g'mara (M'gila 17) says he spent the summer season. Thus, he got there the day before Pesach. That happened the same day he had met Esav.
The previous night, the night of the fourteenth of Nisan, thus, Yaakov met the "man" (or angel). On the thirteenth, then, he sent presents to Esav. This is the start of chapter 32. 32:1 indicates that this is the day after the events of the end of chapter 31. Thus, Lavan said "Ashre" on the 12th of Nisan.
What day of the week was this? Well, 31:24 says it was the day after he got to Gil'ad Mountain, and Rashi to 31:23 says that that was the day after Lavan had found out Yaakov's departure — which, 31:32 says, was בַּיּוֹם הַשְּׁלִישִׁי, Tuesday. So it was Thursday, the twelfth of Nisan.
Of course, Thursday, the twelfth of Nisan, is a fast day, taanis b'choros.
Lavan was part of a group of seven people:
This occurred thirteen years after Yaakov married, so none of his sons were bar mitzva. However, in the presence of nine adults, one boy can count toward a minyan (Orach Chayim 55:4). In 31:51, Lavan realizes "וְעֵדָה הַמַּצֵּבָה, the monument makes a minyan" (as we see in the g'mara (M'gila 23) that "עֵדָה" means "minyan"). Thus, the monument, Yaakov, and one of his sons made the minyan, so Lavan had seven people. Lavan was pointing out that he had a minyan because he realized now that you need one for "Vay'chal".
Lavan's seven people were all fasting:
This we see from Rashi to 31:23, who translates "אֶחָיו", literally "his brothers", as "his relatives". What could have compelled Rashi to do so? It must be Rashi knew Lavan's "brothers" were not really his brothers, because they were all b'choros.