Urgent advice with problematic Lycaste Aromatica

[Jeff9]

Greetings,

I've been growing for a few years now but i'm not very experienced with Lycaste.
The plant in question is Lycaste Aromatica, i received the 2 back bulbs a long time ago and it has never performed really well.

Basically, the two back bulbs are very dark (almost black) and the three front ones are very small, the middle one being damaged severely and slightly rotting and degrading.

The root system is pathetic, from what i can tell most roots are dead or dying so i removed it from its pot to see what's going on.

A while ago it had a new growth on the damaged bulb, but it got infected with little black insects and died off before i found out.

Now taking it out of its pot i've noticed what seems to be either spikes or new growths, i assume the latter.
Both growths are growing from the middle bulb which is also the most healthiest.

My question is if anyone with more lycaste experience than me could give me some advice in what actions to take next.

1. How can i prevent the new growths from getting infected with the black insects again (lice?), and will it happen again?

2. Should i leave the remaining roots even tough i assume they're dead?

3. Should i keep the plant intact or slice it up in divisions/backbulbs (both growths are coming out of 1 bulb and i fear the 2 back and front one will die off)

I have been thinking about moving this plant to s/h would it be a wise decision judging by its condition and if so, i assume it will be best to wait untill roots start growing from the growths?

My plan was to put it on a small saucer with some leca and sphag to keep it moist and allow the growths to develop and then move it to S/H

Please give me some advice as i'm unsure how to handle this lycaste.

The growths are marked with red circles on the photographs

Thanks.