Sand doesn't always improve drainage - it can actually fill the gaps in a peat-based compost and make it worse.
Building (bricklaying) sand is the worst, silver sand is dubious, sharp sand is much better, but even better is to sift sharp sand in a kitchen seive and discard what goes through (still useful for its original purpose or to level a lawn) - so you end up with fine grit.
A good rinse makes sense but don't believe scare stories about salt in sand - salt would interfere with the setting of cement so there's very good reason to keep it out of ordinary sand.
Simplest is to use 10-20% perlite or vermiculite. If extra weight isn't an issue you can buy in grit or gravel.
Other things to consider - citrus don't really have root hairs so they are much more fussy about moisture, especially in low temps - I lost 10% of my citrus every year until I started watering only via capillary matting in winter.
Don't pot on in big jumps - that would encourage fatal waterlogging in the un-colonised area. I also put vertical columns of perlite in the new soil to guarantee a drainage path - though I have no positive proof they make any difference.
Don't use tomato fertiliser - citrus are different - they like more nitrogen than potash at all times, especially in summer. They prefer the acid side of neutral too. Composts and fertilisers designed for ericacious plants can be used at 25-50% with good results.
Cheers.
