The Rashbam and Ibn Ezra (on 19:11) explain that dealing falsely means denying that you have money that was given to you and the Rashbam quotes as a proof 5:22 which also has the phrase not to deal falsely (ve-kichesh) in reference to a pledge. Ibn Ezra adds that dealing falsely is also when somebody knows some information but does not testify.
With regard to lying, the Rashbam writes that it refers to lying about a loan, while the Ibn Ezra writes that the lying refers to making a false claim for money. These commentators seem to be explaining that the difference between dealing falsely and lying is whether the case concerns a pledge or a loan. This is a difficult distinction since the verse does not refer to different items but to different prohibitions.
This same term for dealing falsely also appears by Sara when she was accused of laughing and she denied laughing, va-tichachesh, Bereshit 18:15. Similarly, the case in Vayikra 5:21 is when a person denies having a pledge.
I would suggest that the prohibition in 19:11 of dealing falsely is passive lying, that a person is falsely denying an accusation, while the prohibition of lying is active lying, to fabricate something that never happened or is not true.
Rashi (on 19:11) quotes from Torah Cohanim, that the prohibitions recorded in 19:11,12 form a sequence of events: if one steals, then this will lead one to deal falsely, then to lie and then to swear falsely. In our discussion on Vayikra 5:21,22, “False claims, gezel and genevah,” I propose that genevah was where one stole an item and could not claim ownership of the item, as opposed to gezelah where one stole an item and also falsely claimed ownership of the item. Following this idea, maybe one could understand the sequence of prohibitions in 19:11,12 in the following manner. First one steals and as he/ she cannot claim ownership of the item, then one "deals falsely" that he/ she denies that he/ she stole the item. Afterwards he/ she lies by fabricating a story to show that he/ she could not have stolen the item, a false alibi, and then finally he/ she swears to "prove" that he/ she did not steal the item.
Rashi (on 19:11) quotes from Torah Cohanim, that the prohibitions recorded in 19:11,12 form a sequence of events: if one steals, then this will lead one to deal falsely, then to lie and then to swear falsely. In our discussion on Vayikra 5:21,22, “False claims, gezel and genevah,” I propose that genevah was where one stole an item and could not claim ownership of the item, as opposed to gezelah where one stole an item and also falsely claimed ownership of the item. Following this idea, maybe one could understand the sequence of prohibitions in 19:11,12 in the following manner. First one steals and as he/ she cannot claim ownership of the item, then one "deals falsely" that he/ she denies that he/ she stole the item. Afterwards he/ she lies by fabricating a story to show that he/ she could not have stolen the item, a false alibi, and then finally he/ she swears to "prove" that he/ she did not steal the item.