Lagging Tail doesn't make you slower, it always forces you to go last in your priority bracket; the only way you can out speed something with Lagging Tail is if you use an increased priority move or your opponent uses a decreased priority move.
As for checking Chlorophyll, get a Pokemon around the same level as those Ivysaurs, that does NOT have Chlorophyll itself, and use Sunny Day. Make sure the Pokemon out speeds the Ivysaur in the beginning, and just test it out by using a move or two (use a powder move, maybe, since grass types are immune to them). Then use Sunny Day, and see if the Ivysaur out speeds you. If it does, it has Chlorophyll.