Early on a surprise horsemen rush can be fatal if you are not prepared for it.
I'd say that if you are near Tasunke you should start building up a decent military early even if it means cutting back abit on building other non-essential buildings like wonders etc. That usually is the best way to prevent a Hippus rush.
Needless to say, as the Luchuirp, you should focus on getting good ol' Barney up to combat V ASAP. With empower V wood golems, you should be really getting very good odds even against battle-hardened horsemen.
Horsemen are str 4 after all, and
cannot gain defensive bonuses--so use that to your advantage.
Even a combat V horsemen would only have a str of 8, and a wood golem (base 6) with empower V, would have a str of 9.
So once you kill off those veteran horsemen, the remainder of the stack (which say only has combat III), would be easy to mop up.
The problem really comes if you are surprised by a huge invading stack and your military is too weak. (that's why I've advocated a decently large military as deterrence earlier)
However, as I've mentioned in the comparison of modified str, garrisoned wood golems are definitely hard to kill by horsemen--but beware of their withdrawal abilities through flanking.
Golems might have good high str, but they are impotent when it comes to regaining str through purely healing.
Enchantment Adepts for Repair are absolutely
essential for the Luchuirp, so grab KoTE early on. A simple earth I wall of stone would also help increase the defensive bonuses of your cities.
With enough Adepts on the field, you'd actually find that Luchuirp's golem army actually recovers much faster, than any other generic civ needing to heal a few turns with medic II priests.
Thats my take on the Luchuirp against the Hippus in the early-mid game.
Many of the other suggestions found in this thread are not Ljosolfar specific, and can be applied or modified to fit into the Luchuirp's case. (for eg. not building roads near raider civs)