The best way I've found to link lapis. Is for lower level grinding equipment. Just use level 3's and 2's if you can find enough. Stock up on the gem you want to link. Wait for bless or near bless. Then just start linking.
For Level 4 or Dual Lapis. What you want to do is make sure you have four or more of the same gem. Try to link 4-5 at bless or near full bless. As long as you are getting 16% to link you are good. Make sure to check that it says 16% before you start linking. If you fail all 4-5 lapis. Stop trying to link and wait till next bless. You don't want to blow through all of your money at once.
When it comes to level 5 lapis. It really depends on which ones you are linking. For the cheaper Hp, Mp, Sp etc. Just do what I recommended above. 4-5 lapis during bless or near full bless then stop. For the more expensive 5's. You are better off trying to link 1-2 with a Linking or Op Hammer.
For level 6 lapis. You NEED lucky charms and don't steal them from lucky.
You also need Op hammers or better to link these things. I recommend trying to link just a few of these at at a time.
A rule of thumb for what type of lapis you should be buying. Look at the price of the lapis. If you can buy twenty of those or more. Then its safe to start linking. Don't buy lapis that is outside of your means trying to get lucky with a link. You will just bankrupt yourself.