I have a near mint condition original lcp pistol.  Today i went in and they had a Ruger lcp max for $350
I am not sure new or used but the quick inspection i did looked new.

I like the u notch rear sight and the extra rounds it has over my lcp in about the same size pistol.

With the things noted is there any other difference between my lcp and the lcp max?

Would it be worth to try and trade in my lcp?

Will the lcp max fit my lcp holster?

This is going to be a back up carry pistol my ruger max 9 is my main carry pistol.

If it were me, no.  I have a gen 1 LCP that works just fine.  Not sure the next gen offers all that much.  It's a pocket gun, ten foot range, maybe twenty.  You won't get squat for a trade, Ruger has made a bazillion of those, new they weren't much more than $200.

Mine is my summer pocket carry.

Same opinion. Were I buying into it new, I would consider a LCP II or maybe a max.
I have handled and shot the LCP II and it is certainly a more refined gun but not enough improvement to toss aside my Gen1.

I have several LCPs of all types. The Max is not significantly better than the old LCPs except in round count. My 10-round magazines can actually hold 12 rounds and function just fine, so the LCP Max is a 13-round pocket pistol which is nice.

The Max does work in my LCP1 pocket holster but it's tight. YMMV.

I disliked my original LCP so much I gave it to a friend for free. My pocket gun for when I can't carry a real gun is now an LCP Max and I like it quite well. The trigger is much better than the gen 1 IMO, but I don't much like heavy double action trigger pulls. That in conjunction with the improved sights and I'm much faster/accurate with the Max compared to the OG LCP. And the added capacity is nice. As to the holsters fitting, that depends. Any of the soft fabricate/leather/flexible ones stand a chance of fitting both, but the kydex ones is unlikely in my experience. I'm sure there are some exceptions to that rule, I just havent had one that would.

I only use mine for running. Had to paint it to stop it from rusting. I wouldn't carry it for anything else other than running. Mine is probably worth less than nothing

Lcp max uses LCP II holsters, not the original LCP holsters.
Trade value on an old LCP is maybe $100 ish, just keep it as it will still have it's place for discreet carry.

Like the others have said, I would not trade it in as you will get nothing for it. I will say the LCP II is quite a different gun than the original LCP I owned and a good upgrade. If you like the LCP Max, I would get it if the price isn't insane. One nice thing about the Max is that Ruger uses real sights, which is a game changer on these little guns. I had the LCP Pro and with real sights, it shot like a laser. A big difference over the standard model.

I’ve had an original LCP for some time now. I thought maybe I was missing out by not upgrading to a II or Max. I had a chance to shoot my LCP and my FIL’s new Max back to back this weekend. I just did not care for the Max. Didn’t like the trigger. Didn’t like it in my hand. Made me fall in love with my LCP all over again.

I think im in the minority here when i say that i havent ever found a lot to complain about with the original lcp. It does the job it was designed for very well. i wont ever get rid of mine.

That said, I havent handled or shot an lcp max.