After a strong acid reacts with pure water will its pH always be a bit less than 7?

You are adding H+ ions to neutral water (not really a reaction I think)so yes

bit less? It can be easily be pH of 2 (lemon juice)or less (pH=0 for battery acid).

The pH of a solution depends on the concentration of hydrogen ions (H+) in the solution. When a strong acid reacts with pure water, it will increase the concentration of H+ ions in the water.

To determine the pH after the reaction, you need to consider the strength of the acid and the initial pH of the water. The initial pH of pure water is 7, which represents a neutral solution.

If the acid is very strong, it will completely dissociate in water, resulting in a high concentration of H+ ions. As a result, the pH will be significantly lower than 7, indicating an acidic solution.

However, if the acid is not very strong or is diluted, the concentration of H+ ions will be lower, resulting in a pH that is slightly less than 7 but still potentially within the neutral range.

To precisely determine the pH after the reaction, you would need to know the concentration and dissociation properties of the acid used, and then perform a calculation using the appropriate mathematical equation for calculating pH.