I looked first at bears to get a handle on this question, because it is well known that bears get a significant part of their caloric intake from berries. I should have looked first at berries!
According to Blueberry Nutrition Facts, one quart of blueberries has 340 calories.
Let's assume that the lost person of the Q expends 4,000 calories per day trying to get unlost. Let's also assume that he or she started out, like most of us, a little bit too well fed, so some of his caloric requirements are met by body fat.
In one month of being lost (probably a large overestimate), assume 2,000 calories per day of body fat are mobilized, 62,000 calories for the month, which is the equivalent of 18 pounds. (One pound of fat has about 3,500 calories. Ignore mobilization efficiency.) Unless the person started out extremely thin, losing 18 pounds is not a serious problem.
In that month, the person has to eat 2,000 calories per day of berries to make up his 4,000 calorie per day requirements. That is 6 quarts of blueberries per day.
How long does it take to pick 6 quarts of blueberries? According to Stewart's Berry Patch:
An experienced picker can generally pick about 8 - 10 pounds of
blueberries in an hour. This is the equivalent to filling two plastic
4 litre ice cream buckets. In order to pick this many berries in an
hour, one needs to be using both hands.
This, of course, is on a berry farm, where the berry bushes are extremely close together and bred for high yield. But it suggests that if you hit a dense patch of blueberries, you can easily pick 2,000 calories worth in a few hours.
But the catch is: There will be bears in that berry patch.
So the answer to the question is: if you are in an area with abundant berries, you can easily survive for the length of the berry season, (possibly without loss of weight) if you can survive the bears. If you are in an area with only scattered berries, you probably cannot get 2,000 calories per day (6 quarts per day) from berries, and will need nuts and even more holes in your belt.
TLDR: The original version of this answer used data about grizzly bear caloric requirements, black bear berry consumption and human caloric requirements to get an answer of 10 quarts (2.5 gallons) of berries per day for 2,000 calories per day, as opposed to the more direct calculation of 6 quarts per day. I estimated an error bar of a factor of 2, and the direct calculation (above) was 60% of the baroque calculation.
I used the following data:
From The North American Bear Center:
Bears around Ely [Minnesota] gain weight most rapidly during July and
August when berries and hazelnuts are abundant. When the berries run
out in September, there is little else to eat. The bears usually
enter dens in September or October.
According to Animal Answers, grizzly bears eat about 20,000 calories a day. The answer from The North American Bear Center (link above) estimates that black bears eat about 30,000 berries a day.
Using a rough grizzly/black bear calories per day to berries per day conversion, the person has to eat roughly 3,000 berries per day.
According to Produce Converter:
The size of these berries ran between .25 to .5 inches in diameter. We
found that a 1 pound container (450g) holds about 3 to 3.5 cups or 195
to 210 fresh blueberries. For a 1 quart measurement you would need to
purchase about 1.5 pounds which equals about 4.25 cups.
So 300 blueberries need a one quart container. 3,000 blueberries thus occupies 10 quarts or 2.5 gallons.