Map from Google - Leipzig

In Leipzig, a city of eastern Germany, in the Land of Saxony, the climate is moderately continental, with cold winters, in which the average temperature is around freezing (0 °C or 32 °F), and moderately warm summers, in which daytime temperature hovers around 24/25 °C (75/77 °F).
Here are the average temperatures.
Average temperatures - Leipzig
LeipzigJanFebMarAprMayJunJulAugSepOctNovDec
LeipzigJFMAMJJASOND
Min (°C)-2-21491214141062-1
Max (°C)3491419222524191484
Min (°F)282834394854575750433630
Max (°F)373948576672777566574639

The city is exposed to both cold and warm air masses, so the weather and the temperature are highly variable. During the warm season, from May to August, thunderstorms can break out in the afternoon.
Precipitation amounts to 535 millimetres (21 inches) per year, therefore it's not abundant, as is common in Eastern Europe, but it's well distributed over the seasons.
Here is the average precipitation.
Average precipitation - Leipzig
LeipzigJanFebMarAprMayJunJulAugSepOctNovDecYear
LeipzigJFMAMJJASONDY
Prec. (mm)302540404555706550304540535
Prec. (in)1.211.61.61.82.22.82.621.21.81.621.1
Days87879999879999

Winter, from December to February, is cold, with average temperatures hovering around freezing. Actually, during winter, different situations can occur.
There may be relatively mild periods, in which Atlantic currents prevail, it can rain and the temperatures can exceed 10 °C (50 °F); in these cases, however, wind and humidity can increase the feeling of cold.
Then, there are situations in which a high pressure system dominates, and the weather is cold and gray, with night frosts and daytime temperatures around freezing, or even a little below. Later, when the westerlies start to blow again, flowing above the layer of cold air, they can bring snow, sleet, rain mixed with snow or rain that freezes.
At other times, cold air masses of Siberian origin may cause snowfall and frost, sometimes intense. In the past, once every few years it happened that the temperature remained below freezing for an entire month; in recent years it has become more rare, however, sometimes freezing periods still occur, which may last for weeks, and in which the temperature can drop to -20 °C (-4 °F).

Spring, from March to May, is a season characterized by an unstable weather, in which the first warm days alternate with the return of cold weather. March is often a cold month, with frequent snowfalls. In April, cold periods are still possible, with late snowfalls, especially in the first half of the month, but also the first mild days, in which the temperature can reach 20 °C (68 °F), especially in the second half of the month. In early May, it can still get cold; with the passing of days the first warm days occur, in which the temperature can reach 25 °C (77 °F), and the first afternoon thunderstorms can occur.

Summer, from June to August, is pleasantly warm: daytime temperatures hover around 22 °C (72 °F) in June and 24/25 °C (75/77 °F) in July and August. However, nights are cool, and sometimes even a little cold. Atlantic depressions can arrive in this season as well, bringing some cool and rainy days, while in periods of good weather the temperature can get close to 30 °C (86 °F). There is some variability from year to year: there may be summers characterized by long warm and sunny periods, and others in which cool and rainy weather is more frequent. However, some hot days, with highs around 28/30 °C (82/86 °F), occur almost every year; occasionally there can be even waves of intense heat, with highs about 36/37 °C (97/99 °F), though they usually last only a day or two.
On sunny days, thunderstorms can break out in the afternoon.

In autumn, from September to November, the flow of Atlantic fronts, which had never completely stopped, resumes with greater frequency, although sometimes a period of good and unseasonably warm weather can occur, a sort of Indian summer, called Altweibersommer, in September and sometimes in October. Generally, September is still an acceptable month; cold and gray weather usually arrives in the second half of October or more likely in November, when the first snowfalls are also possible.

Leipzig

The amount of sunshine in Leipzig is never great, however, it is passable from May to August, when the days are also very long, and there are about 7 hours of sunshine per day. From November to February, the sun rarely shines and the days are short.
Sunshine - Leipzig
LeipzigJanFebMarAprMayJunJulAugSepOctNovDec
LeipzigJFMAMJJASOND
Sun (hours)234677775422

When to go

The best time to visit Leipzig runs from mid-May to late September. In September, the days are shorter than in the previous months, but the weather is generally pleasant and crisp. However, even in summer it's better to bring some heavier clothes, like a sweatshirt or sweater, and a light jacket for cooler evenings. It may also be useful to bring an umbrella or a raincoat, for rains and thunderstorms.