Banishment forces rerolls of successful ward saves so that Light spell can thin them out while you are waiting for them to get in CC range. A Salamander will do okay, though they will drop half as fast as other elves, they still have to take their Panic test (which they will probably pass unfortunately). In close combat, Phoenix Guard do not drop easily with their mighty Ward Saves. The Lizardmen list really doesn't have anything that can take Phoenix Guard out one-on-one (unless you have VERY deep ranks and are willing to play attrition or are able to get Speed of Light AND Birona's Timewarp on them), so I'd recommend flanking the Phoenix Guard with something, a Skroxigor, Stegadon, Cold One Cavalry, or if you are in a pinch a Razordon or Salamander. Speed of Light should probably be used on whatever is fighting the PG, that'll deny them the rerolls from ASF and make them hit your Sauri on 4s instead of 3. That should drastically reduce the number of casualties you take. Pha's Proteciton and Biorona's Timewarp will help you too but you probably don't want to load up all your buffs on one fight. Since some are bound to be dispelled, why not lead off with Timewarp to draw out the dispel dice? The number 6 spells tend to instinctively worry players.
EotG or chief on a steg with the other tricksters shard. Impact hits plus thunderstomp with re-roled successful ward saves.
Phoenix guard (PG) should not be ripping through either TG or saurus since they are only S4. Horde on horde or with roughly equal models fighting, the saurus should be coming out ahead or near even with PG and since they are cheaper you can win a war of attrition. TG are similar but about equal points. Given that PG are not that choppy, I will proceed based on the HE unit that ripped through your army being the white lions (WL), which definitely can chew through lizzies with ease since they have S6, ASF and re-rolls to hit. WL are also stubborn so grinding with them won't work. The best bet is to magic missile them (their lion cloaks DO NOT add to the armour save vs MM or direct damage as per their FAQ - many HE players either "forget" or do not know this) and use sallies since they will only save on 6. If you must engage them in combat, an effective tactic is to sacrifice a unit so that you can get a charge in on both flanks. A unit contacted on both flanks cannot reform and thus this will limit the number of attacks to only those in direct contact while you strike back with many more attacks. Ideally, a steggie just touching the corner of the unit with a ranked unit on one side is perfect since only one WL can attack it per round while it can thunderstomp the elves into the mush.
what stonecutter said. phoenix guard (fighting with two attacks per FILE) will do on average 0,49 wounds per file. sauruses (fighting with three attacks per file) will do on average 0,42 wounds per file sauruses do rougly the same damage, but are much cheaper. in any case it should be no slaughter in the favour of the PG, unless they were buffed hugely and you were not. in that case it is not the PG that is the problem but the wizard. any unit can be buffed to a killing machine with enough magic. On a related matter, white lions and sword masters will do the exact same amount of damage per file against sauruses. both will murder your sauruses in a fair fight, so do not give them one