Really the best avenue is to have high enough stats that you can run through the Phases before the Eidolons can attack. the other options are all going to be switching to a different Warframe or Focus School, which will make it much slower overall.
Short of that, you can try not standing directly under the Eidolon so that if it stomps the ground it will deal a lot less Damage to the Lures. also Killing Vomvalysts rather than letting them shoot at the Lures.

If you don't want to change Warframes/Focus and those remediations aren't enough for you, increase your Damage more. move through both Shield and Health Phases in a single shot/hit.
Or, if you don't want to do all of the jobs at once, then don't play Solo. you don't have to, there's plenty of Players. if you're sure that you know what you're doing and you want to look for others that definitely do, you can always use Recruiting Chat.

I hunt Eidolons with Trinity for this reason. Yeah, it's slower, but it's the safe option; a Trinity built around her 4 is almost guaranteed to keep the lures alive.

I eventually took to not grabbing lures until the last limb. Enough little buggers rush up to fill the lures as you do the last limb, and the lures only take damage that short bit of time. Made it consistent to keep the lures alive. Probably not for everyone, but works for me.

If I can't find a setup that works for me and hoarding too many lures doesn't work I'll see how I go with that. Cheers.

cycle through limbs fast enough that you don't need to worry about them/just step aside if the eidolon slams and the lures will follow you/bring a healer like trinity or wisp

ideally you want to instantly break shield and limb so garry doesnt have time to throw out the light beams but if he does u just move them out of the way (easier said than done with their shitty ai but yeah). thats pretty much the only point lures are in danger of dying. you can drop ancient healer specters to make them take close to no damage but the specter itself dies super fast so youll have to keep refreshing it which really isnt worth it.

you can try Oberon

Smite adds radiation damage to your weapons, the grass protects you and lures during energy spikes . Renewal in bursts adds armor as well

In case you find yourself struggling during hydrolyst , the ancient healer specter also helps, but you might to have drop the specter often because it dies quickly

I'll see how I go with another set up first using vazarin then will give oberon a shot, cheers.

I have over 100 of them so should be fine with spectres then at least