Why couldn't they launch the lunar lander/propulsion assembly into orbit separately and then send a manned Soyuz to mate it in orbit? Then go to the moon?

The issue is that these things are all very heavy, and going multiple rendezvous in orbit takes time. This was, however, a method considered seriously by the US and USSR.

So there are two parts here. First, the lunar lander. The Soviet design was 5.5 metric tons, called the LK. Then, the lunar orbiter, the 7K-LOK. The Soviet design, based on a Soyuz capsule, was approximately 10 tons. Both of those are substantially lighter than the American ones, since they were only using 2 cosmonauts (with only 1 landing).

The payload of the Soyuz, though, was only 6.5t. So it's a little underpowered for the orbiter. But that's not the main problem. That's the payload to LEO. You need to get that lander+orbiter (15.5 metric tons) from low earth orbit to TLI (trans-lunar injection, an orbit that brings the spacecraft from a low altitude to one that meets the moon). That's expensive. I plugged in some numbers, for the NK-33 engine, you'd require 39.6 tons of fuel. That's not counting engines and the tank.

So, you'd need two launches of roughly the Soyuz's capacity, plus one that's a great deal heavier. There's no good way of doing that with Soyuz. To do it, you'd need to have the lunar injection in several pieces, with each docking adding mass (docking equipment has mass, too).

So what's the problem doing it in lots of chunks? Well, what order would you do it in? If you did manned capsule first, you'd need to bring food and life support for them to work long enough to bring the rest up. However, bringing the TLI stage to orbit in pieces has its own problem. Cryogenic propellants boil off over time. Liquid oxygen and kerosene was what the Soviets would've used (the US used liquid oxygen and liquid hydrogen for this stage). If you couldn't do the docking fast enough, you'd lose your fuel. You could use more stable fuels, but they're substantially less efficient and either difficult to control (solid fuel) or hazardous (hypergaulic propellants). A more reasonable number of pieces meeting would've still required a rocket much larger than any the Soviets had available.

Anyway, the US considered this approach, launching several vehicles. It would've used one rocket to essentially send an empty tank into orbit, which would then be refueled over time. But other approaches won out. First direct ascent, which would've required a rocket even larger than the Saturn V, and finally Lunar Orbit Rendezvous, which is how the Apollo missions got to the moon.

For the specs of the Russian vehicles, see here:

http://www.astronautix.com/craft/soy7klok.htm

http://www.astronautix.com/craft/lk.htm

http://www.astronautix.com/lvs/soyuz.htm

For a piece on the history of the American selection of the lunar orbit rendezvous option, see here

tl;dr The pieces were too heavy to be brought up by Soyuz, and there are drawbacks to bringing the craft up in chunks, especially the number needed to use Soyuz.

You may try crossposting to /r/askscience