Lubeck's northerly latitute and location near the sea combine to produce a mild climate that is cool in the winter and warm in the summer. The warmest months are July and August, when average high temperatures reach into the lower-70s (lower 20s C). Average lows during this time are in the upper-50s (15 C). It can get cool at night during any time of year, so you may want to bring a jacket or a sweater even if you are visiting during the height of summer. The coldest period for Lubeck is during December, January and February. Average highs are only in the upper-30s to lower-40s (5 C). Lows get down to a little above freezing, which means that winters are cold, but not extremely so.
Lubeck is pretty wet, and receives a significant amount of rainfall throughout the year. Every month averages above four inches of rain. The wettest month on average is August, which receives about ten inches of rain. April is the driest month, though it still gets about four-and-a-half inches of rain on average. Snowfall is possible during the winter, but only for brief amounts of time, and it usually melts within a couple of days.
The bottom line is to prepare for rainy weather whenever you are visiting Lubeck, just like you would if you were going to visit London, which receives a comparable amount of rain.
For a 5-day forecast, check the BBC weather site, here.