Hamburg to Lubeck options

There are about 47 daily trains running from Hamburg Hbf to Lubeck Hbf. Look at www.bahn.de for schedules and fares—they are all there.

Thank you, I was looking at rome2rio and Omio which I have found to accurate in the past. bahne.de is where I should have started.
As I will be traveling on to Berlin and Dresden, do you think a monthly pass would be a good idea?

Local trains every 30 minutes. If 2 to 5 people, a Kleingruppenkarte is 44.90 EUR covers you all day

As I will be traveling on to Berlin and Dresden, do you think a monthly pass would be a good idea?

Do the math. With a monthly pass, assume you are referring to the Deutchland Ticket, You will be restricted to local trains. Since the current express route from Lubeck to Berlin is closed, that really does not effect that leg. It will make the Berlin to Dresden leg longer with more train changes

There are high-speed train tix for December now on sale for €35 from Lubeck to Berlin ( 3:45) and from Berlin to Dresden (2 hrs.) for €18.

Hamburg to Lubeck is about €10.
So, no need to mess with the Deutschland Ticket.

(Prague is only 2:15 beyond Dresden).
Buy your tix as soon as you have your itinerary nailed down.

Cheers!

With Omio you will also find Bahn connections. It is a German company, so they had already integrated this before they renamed their company a few years ago.

For local public transport in Hamburg use https://www.hvv.de/en.

I just traveled Hamburg to Lubeck about a month ago and there were lots of trains. No problems except on the return trip there were some cancelled trains due to track maintenance, but using the fairly reliable Dbahn app I simply adjusted my schedule to catch the next train an hour or two after the cancelled one. It would also show any replacement buses for the cancelled trains but generally I avoid those as they are often slow and packed like sardines. I used the Dbahn app constantly over a month long trip around Germany and found it to be very reliable and accurate.

packed like sardines

This keep us people living here warm; autumn means it seriously to prepare winter. The replacement traffic will likely end in May 2026.

Mark-
I did a day trip from Lubeck to Kiel to see the Uboat (which is actually in Laboe - a suburb of Kiel I guess), and on the return trip to Lubeck, for some reason, there were no trains running to Lubeck so I had to take a replacement bus to a smaller city/town to catch a train. What a crappy experience, 3 buses roll up, all with paper names of where they are going jammed in the window, drivers who don't want to answer any questions, because some buses were direct and others were not - stopping everywhere even though no more people had room to get on, and worst of all they were packed so full that no more people could get on even standing. Then an hour or so to the town. I had a guy's packback stuck in my face the whole way. Not the end of the world I guess but what a pain compared to taking the train