Is the train station within walking distance?

Yes, if you are mobile and not encumbered with too much luggage. Must be a few hundred metres.

It's easy. Turn right on exiting Babylon and go up to the top of the soi (85 meters). At the T-junction, turn left into Sathorn Soi 1. This is being resurfaced at present and so is a bit of a mess. Walk along around 150 meters until another T-junction at the main road - South Sathorn. Turn right. After about 70 meters you come to entrance to the MTR (Entrance 2).

FH, how long do you think this would take most people?

 

Also, once you do the MRT, is it easy to get on the Skytrain?

It depends. Some people could probably run the whole distance, complete with backpack. Others couldn't even walk it, due to age, lifestyle choices or simply too much luggage. Those who can walk it generally benefit from doing so.

 

Connecting to the Bts at Sala Daeng is very easy. The stations are adjacent and they even have some escalators.

As z909 says, it depends on age, health etc. I'm in my early 60s and I regularly walk home from Life Centre (which is right at Lumpini Exit 2) along Sathorn Soi 1. From the MRT to Babylon would take me no more than 8 - 10 minutes at a normal walking pace.

 

Connection from Lumpini MRT to the BTS Skytrain depends on where you want to go. If you want to connect at Silom/Saladaeng, there is a bit of a walk. You come up from the Silom MRT, then go up an extra escalator and walk about 100 meters on an overpass directly in to Saladaeng BTS station.

 

If you are going to Sukhumvit, it's definitely easier to take the MRT in the other direction to Asoke/Sukhumvit (3 stations). There is a very easy connection there with less walking.

Be advised that both MRT and BTS don't operate between 12 midnight to 6 am.

I have done this walk only once some years ago in the full afternoon sun in 12 min.. In MRT i got a shock from the ice cold aircondition. During daytime never would do again.

Walking up that soi from the Sukhothai Residence (across the road from Babylon) the other day, I noticed that it is about 150m to Sathorn Soi 1, a bit further than I estimated in post #3. But that should only add a minute or so to the total walking time. The weather now has started to cool down and so the walk should be relatively pleasant for a few weeks.