I’ve always had a lazy. When I was a kid it was very bad. I’m left eye dominate which sees very well up close and my right eye is good at longer distances. I constantly switch back and forth between the two eyes but can’t get stereoscopic vision even though both eyes are in alignment.
My suggestion to you is to force yourself to alternate using your lazy and dominate eye throughout the day. While reading a book alternate eyes with each page.
Try this: Look in the mirror through your dominate eye with your hand over your weak eye. Take your hand away and notice how your weak eye drifts off. Now put your hand over your strong eye and look in the mirror through your weak eye. Keep looking through your week eye and take your hand away and notice how both eyes are now looking straight forward. Now practice looking in the mirror with no hands involved by just alternate eyes. Notice again how your eyes appear when looking through each individual eye. Also practice alternating eyes throughout the day focusing on up close objects as well as long distance. This technique has worked well for me.
When you talk to people remember to look at them through your weak eye and they will see both of your eyes appearing to look straight at them.
The key I think is to work your weak eye more and it will get stronger. You may be like me and never have eyes that work perfectly together but your eyes will appear normal to others and that should give you some more confidence.