1997 Mazda protege transmission, Hard shifting from 1st gear

I would try a flush. If its set up like my 96, and it likely is, changing the trasmission gasket and filter will be difficult. Mine has a medal plug on the bottom and takes an allen wrench, and possibly a breaker bar. If you take out this plug, drain, flush then refill via the dipstick tube and a funnel, it may help. You may need to do this a couple of times due to fluid still in the torque converter, pan, etc.
Lucas is good stuff, I would add it again when I was done. The tranny fluid should be pink, mine looked like used oil black before I flushed it.
Also, when adding the new fluid, shift slowly up and down through all of the gears to lube well and check your fluid levels after 100 miles or so, as sometimes a bubble will form and make it look full....then not after it pops.

There is a repair kit for the AT in this model that fixes the problem of harsh shifting from first gear. It is a spring for one of the AT valves. It is available at a Mazda dealer and there is a service bulletin that accompanies it. I wouldn't recommend any type of additive in the ATF since I had the experience of it foaming in the torque converter at high speed. Clean ATF is high detergent already, the additives just swell the seals which are not a problem with this transmission. I have 300K on mine and it is still going without an overhhual, just changing the filter and fluid when the color changes.

You might check your mounts. When an engine is cold, it has a higher idle, hence more torque when shifting. If a mount is broken, it will feel like a hard shift. Raise the hood. Start the car. Through the windshield watch the engine. Put the car in gear and hold the brake. Slowly try to accelerate. If the engine raises up then flops down when you let off the gas a mount is broken. Try it in both forward and reverse. Careful to lock on the brake so you do not move and do not give too much gas.