We stayed in the Lysithea a few years ago.
It is as near as damn it the last place going East in Larnaca. (It is really Pyla Tourist Area) We had no complaints when we stayed there.
It has recently undergone a refurb.

There are a few restaurants within easy walking distance (although what was my favourite, Sokrates, is now a gym.) They do a themed night with food and dancing once or twice a week.
There are small supermarkets nearby.
Across the road is the CTO tourist beach with a bar/cafe.
The tourist bus passes right by and you should be guaranteed a seat. The Lysithea is the first pick-up point.

Livadhiotis is where i use t'internet, never stayed there so can't help in that respect. It is almost in the centre of town, 50 mtrs from St Lazarus Church, 50 mtrs from the Prom.

My choice (with a hire car) Lysithea. If no car, Livadhiotis would seem the better option.

Mark

Just remembered re the tourist bus, it used to stop running late afternoon, but when we were over last September they seemed to be running well into the evening.

Thanks Mark, for that info, most useful. Now I hope Mum can come to a decision!!