You can't hear the low frequencies in the second set of speakers because (one or a combination of these):
1) Bad low frequency response in the second set of speakers
The second (bad) set doesn't have a good low frequency response. This is very common, specially in cheap and/or small speakers. It is as if you filtered the low frequencies with a HPF, the speaker is just not able to play those low frequencies correctly, if at all.
2) Bad low frequency response in the first set of speakers
Your first set of speakers (the good monitor ones) are accentuating those low frequencies, so when you switch to another set those low frequencies are not accentuated anymore, which can be heard as a loss of amplitude in that band.
The room, your position, and the position of both speakers. Are both set of speakers in the same room? Different rooms color the sound differently, rooms have frequency response too. As the speakers, one room can accentuate the lows. Make sure you are listening to both sets in the same room.
Also, even if they are in the same room, orientation and position can drastically change the sound, so make sure both sets are correctly and similarly positioned. You can read more about that here, here, and here.
Do I have to work on MIX steps or MASTERING steps? It's hard for me to discover the problem on monitor speakers because I can't hear the problem.
This can be tweaked during mastering, but with limits. You can affect bands, but not individual instruments. Because of this, you want to carve the frequency dynamics and curve correctly during the mixing phase.
To get the speakers and room somewhat out of the equation, listen to the mix in the set of speakers (or headphones) you normally listen music with, in the room you normally listen music in (not applicable for headphones). You know that room, you know those speakers. They can't lie to you. Tweak the lows using that system as reference.
Use a reference track. Get a track that you like and is similar to yours, one that was mixed by a great mixing engineer, something commercial class 1 quality. Pay attention to the lows, and tweak the lows in your track to approximate the ones in the reference track.
You can also use a reference track for visual reference. Using a tool to visualize the frequency dynamics and curve of both the reference and your track, you can tweak yours to approximate the reference track's frequency curve. For this I normally use either Fab Filter's EQ or the Logic Pro EQ, both provide a visualization tool.
Get to know your pair of monitors and room, so you always have the certainty of what's going on frequency-wise.
About mixing and speakers
As you just noticed, not all speakers sound the same. Some speakers will not be able to play the lows correctly, or maybe the highs, or whatever band you can think of. This is normal. Some speakers will play your track with no lows, some speakers will play it with too much highs, it's inevitable.
You'll need to find a middle ground: a mix that sounds great in good speakers, but also acceptable on other speakers. Play your mix though many different speakers: headphones, earbuds, monitors, car system, etc. Tweak it until you like what you hear in all of them, having the limitations and characteristics of every set of speakers in mind.