Are there readily available models that can handle conditional correlation?
It is totally ok to drop null values here (in your case all the null values of LotFrontage), because this data isn't real. This is a standard part of data preprocessing called data cleaning. If the reason for the null values is known you could do additional steps like imputing or filling, but without this information just dropping them would be fine.
I would be careful changing null to zero however, as this is now creating data (i.e. apartments with zero size front lots).
Finally, you can see from your scatter plot that the relationship is not completely linear, so the linear model may have a large degree of error and/or low R squared values. So it may be more suitable to pick another algorithm for this dataset (e.g. 2D gaussian model).