Relaxed : Free from tension and anxiety; at ease. Relaxed is a positive connotation and is different from inactive because relaxed means your calm and have no stress where inactive is when your not doing anything. Also the difference between lazy and relaxed is that relaxed you have the ability to do stuff your just staying calm and when your lazy you just don't have the motivation to do things.
Inactive : not engaging in or involving any or much physical activity ; not working; inoperative. Inactive is like a neutral word there's really no emotion in the word its just stating that your not doing anything. The difference between inactive and relaxed is that relaxed your just at ease and have nothing to do but relax but when your inactive you just aren't doing anything and you really aren't calm. The difference between inactive and lazy is that inactive is lazy you don't want to get up or do anything you just want to sit there but when your inactive you already are just doing nothing.
Lazy : unwilling to work or use energy. Lazy is a negative word because your unwilling to do things because you just don't want too because your not hard working. The difference between lazy and relaxed is that relaxed your calm not worrying and just at peace, lazy you don't want to get up you just wanna lie down because you don't have any motivation. The difference between inactive and lazy is that inactive you aren't doing anything at all and lazy you don't wanna go do anything.