I was going to reply to you before but decided against it since you're still relatively new to the show and thought you'd eventually put more pieces together...so if you want to let that happen, then don't read my lengthy reply below.
Wait up a second here, are we watching the same show?
Varys was always pro Dany and always pro Ned.
Varys never did anything to pin the Starks against the Lannisters, or cause the "wolf and the lion" to be at each others throats. During that conversation when Arya is chasing cats, Illyrio says, "one hand died, why not the other?" to which Varys replies and says "This hand is not like the other". Varys had nothing but respect for Ned. He'd often secretly talk to Ned in the cells, bring him wine, water and of course his reaction to when Joffrey called for his head implied that he really didn't want it to happen.
Also, the assassination attempt on Dany was Varys covering his own ass. He sent the order because he had to, but also sent word to Jorah to look out for poisoned wine, you think Jorah figured that out himself? Of course not, he even got the letter in that same episode. She was never at risk.
And they were always plotting to put Dany on the throne, They even say. Khal Drogo won't make his move until his son is born. Illyrio and Varys are the one's who set up Dany with Drogo with each other.
Finally, if he didn't know about LF being involved in the death of Jon Arryn, then it was because it was LF, almost his equal. But he probably did know, but to what benefit would revealing that information be? The plan was always getting the Lannisters and Baratheons out of power. His death worked in their favor, only that it all happened too soon, and Illyrio even says so.
Varys was always for the realm.
EDIT:
Didn't want to double post, but wanted to share this.