All Praise to Allah Subhanahu wa Taala and blessings of Him be on Prophet Muhammad peace be upon him His family and companions,
It is not allowed to pray while sitting unless necessary like ill or not able to stand as Qiyam (Standing) is one of the essential of salah ,Laziness is not the condition considered to pray in a sitting way.
Abdullah bin Buraida:Imran bin Husain had piles. Once Abu
Ma mar narrated from `Imran bin Husain had said, "I asked the Prophet
(p.b.u.h) about the prayer of a person while sitting. He said, 'It is
better for one to pray standing; and whoever prays sitting gets half
the reward of that who prays while standing; and whoever prays while
Lying gets half the reward of that who prays while sitting.'
The first hadith you quoted is showing importance of night prayers ,When Rasulullah salAllahu alayhi wasallam became so ill even then he was not skipping his night prayers and laziness here means exertion beacause of the sickness not the usual lazinees like ours.As Allah swt has asked him to take rest in Surah Muzzammil because he used to be in Qiyam all the night and did not get the time to take rest,
O you who wraps himself [in clothing],Arise [to pray] the night,
except for a little -Half of it - or subtract from it a little(73:1-3)
So if someone has the valid reason he is not able to stand he could pray while sitting if he could not sit then he could pray while lying,
Narrated `Imran bin Husain: had piles, so I asked the Prophet (ﷺ)
about the prayer. He said, "Pray while standing and if you can't, pray
while sitting and if you cannot do even that, then pray Lying on your
The second hadith you mentioned is actually emphasizing and providing the proof to do qiyam while prayers and "to sit down if tired" in that hadith does not indicate to sit during the prayers but to start prayers after some rest wallahu a'lam,
Also see this for more,
Allah Swt and His Messenger knows best.