How to connect tube pre amp section of Hybrid amp to second Integrated amp ?

Your diagram is correct! Connecting two pairs of speakers to Amp 2 will double its current draw and cause it to run hotter.

Personally I would not feed an integrated amp's output into another integrated amp's input.   I see all kinds of volume matching problems and distortion.    That arrangement is referred to as cascading and it often yields poor results.    Won't hurt anything but is not really desirable.    

@oddiofyl : the OP is going to connect the tube preamp of Amp 1 to the "main-in" of Amp 2. Thus avoiding Amp 2's preamp stage. No problem! 

Sorry,  main in no problem but second EQ will not get anything from second amos pre out....

Yes, EQ2 will not be used to enhance the signal & there's nothing connected to the Line Out of EQ2. I just need to get the signal to EQ2 to get the EQ analyzer running. Do you see any issue there with reference to the connection diagram?

@oddiofyl  is correct. With nothing going into the line input of Amp 2, there will be no signal at the Amp 2 line out to feed EQ 2.

oddiofyl & cleeds, I got it - looks like my EQ2 lightshow has a problem..🤔

Any suggestions to include it without taking any unnecessary risks? Thanks, guys. Appreciate it.

I suppose you could use a Y-connector, such as on the Amp 1 pre-out.

Well, you have a very interesting science project, you are just stacking a bunch of mid-fi vintage gear into a giant chain. Each time you process the information your signal gets degraded. Can it be done, sure. The safest way is processing the signal out of your source. It kinda depends on what the EQ outputs but that is the safest and least destructive way. I’m not really sure on what you are trying to do. That might help me to suggest the best way to do it.

Thanks, russ69.☺

Let me explain what I'm planning to accomplish.. 

When only Lux LV-104u is used, I like the tubey sound that comes from the tube preamp but highs are tad bit eloborated than I like and lows are non-exitsent. I did some research and apparently it's a known issue with Lux hybrids. Meddling with the tone controls and use of EQ doesn't improve the situation.
On the other hand Lux A-353 has an overall balanced sound but it lacks the tubey sound. I'm hoping to get the best of both worlds here and also very curious how this setup would turn out. 

Second EQ is purely for visualization. Do you think by stacking I'm bound to lose the clarity and details? Am I better off forgetting the Lux hybrid and getting a dedicated tube pre-amp?

 Sure you can use the one Luxman as a pre-amp. That is often done when one buys a better power amp for their system. Hook that up and give it a try. Forget the EQs for now. I would not spend any money doing this because a $1500 Rogue Sphinx will probably outperform anything you might do with the Luxmans, EQ, or bi-amping.