There are two features that an Inquisitive Rogue (XGtE, p. 45-46) gains:

Ear for Deceit

When you choose this archetype at 3rd level, you develop a talent for picking out lies. Whenever you make a Wisdom (Insight) check to determine whether a creature is lying, treat a roll of 7 or lower on the d20 as an 8.

and

Insightful Fighting

At 3rd level, you gain the ability to decipher an opponent’s tactics and develop a counter to them. As a bonus action, you can make a Wisdom (Insight) check against a creature you can see that isn’t incapacitated, contested by the target’s Charisma (Deception) check. If you succeed, you can use your Sneak Attack against that target even if you don’t have advantage on the attack roll, but not if you have disadvantage on it.

When invoking Insightful Fighting, does the bonus from Ear for Deceit apply to the Insight roll? I feel as though this might be a bit too strong: if my character has a +2 to Wisdom and takes Expertise in Insight, then this check would have a minimum of 8 + 2 + 4 = 14 at the 3rd level.

However, the use of language

...determine whether a creature is lying...

and

...contested by the target’s Charisma (Deception) check,

where page 178 of the Player's Handbook states

Your Charisma (Deception) check determines whether you can convincingly hide the truth, either verbally or through your actions

makes it feel as though Ear for Deceit ought to apply to Insightful Fighting.

Is an Inquisitive rogue making an Insight check for Insightful Fighting able to apply the benefit of Ear of Deceit to that roll?

You don't benefit from Eye for Deceit when using Insightful Fighting.

If Insightful Fighting involved figuring out whether someone is lying, it would say so. In this case, Deception is a measure of the ability of the target to disguise its tactics. This is not lying in a conventional sense. 5th edition is made to be read in plain English and if this non-traditional usage of the word lying was intended to be included it would say so. In general, features say what they mean.

Ear for Deceit does not work with Insightful Fighting

The rules for Deception checks state:

Your Charisma (Deception) check determines whether you can convincingly hide the truth, either verbally or through your actions. This deception can encompass everything from misleading others through ambiguity to telling outright lies. Typical situations include trying to fast-talk a guard, con a merchant, earn money through gambling, pass yourself off in a disguise, dull someone's suspicions with false assurances, or maintain a straight face while telling a blatant lie.

Lying is one way to "convincingly hide the truth", but not the only way. For example, you could "mislead others through ambiguity" or "pass yourself off in a disguise" without ever lying.

Insightful fighting is just another example among many of a Deception check that does not involve lying.

However, it's worth noting that Reliable Talent (which has a similar effect to Ear for Deceit) does work with Insightful Fighting.