Yes, he plays his weak hand very well in his ties with Russia, that is definitely true. And about Putin unhappy about Lukashenka bragging about Wagner situation also agreed - he actually realized that and started to backtrack a bit.
But on Belarus not sending troops and Putin pressuring - a common misconception that lives on - I am not sure why. If you watch them and think about it - it does not make sense and there is no evidence for that:
1. Belarusian army is small and has no combat experience. There are maybe 5k or so of more or less prepared troops, others are no better than Russian mobilized personnel. They would not have made a huge difference (of course if Kyiv had fallen Lukashenka would have been more than happy to have them participate a tik tok parade there)
2. On the other hand there are significant risks. Lower level personnel is a lot less enthusiastic about the war than their Russian counterparts. Most would obey orders I guess but there would be defections - but above all sending the troops is hugely unpopular in Belarus. Around 90% of population including the majority of Lukashenka supporters are strictly against it. And there is only that much state propaganda could do given that they brandished “no war“ as one of Lukashenka’s prime achievements. This is a home run for opposition forces - and however crushed they might seem - they are still a lot more popular in Belarus than Russian opposition in Russia (and Lukashenka is a lot less popular in Belarus than Putin in Russia)
So it is perfectly feasible that Putin could conclude himself (possibly with the help of argumentation from Lukashenka of course) that the risk reward calculation is unfavorable and as long as he can move his own troops through Belarus it is enough.
Of course you could argue that their calculations and perceptions could be different - but the thing is, if they have some major disagreement it is always revealed by Lukashenka or Putin words/actions. For instance, Lukashenka would act offended, let some remarks slip how russia does not appreciate him etc etc - but there was nothing after the beginning of war. Plus Putin would pressure on economic concessions, deny requests (which was the case even in 2020-2021 although Putin gave Lukashenka full political support in his repressions against his own population) - but after the onset of war he gave Lukashenka all the stuff in terms of economic support that the latter had been asking for years. This just does not fit with Putin pressing and being unhappy and Lukashenka resisting.
Most likely his request was to let through troops, support the war rhetorically and in return get full economic and political support - to which Lukashenka agreed seeing it as the best realistic deal he could get.
