Using a predicted value as independent variable in a regression analysis I know that a certain percentage of error already exists in predicting a measure (ex.: lean body mass) and predicting a cardiorespiratory parameter such as Vo2max using this predicted measure only increases the risk of errors, but I do not know the specific terms or the explanation behind this phenomenon. 
 A: You can use predicted values of anything for any analysis.  Take for example, how students' eyes light up when you tell them that they can e.g. regress plasma retinol concentrations on patient age, and then use the residual, $e_i = y_i - \hat{y}_i$ as a variable representing retinol adjusted for age, i.e., the effect of age is removed from retinol.  You can do anything you want with the new values of retinol with age removed: use in classification analysis, use in clustering, use in PCA, use in logistic and Cox regression, etc.  
For gene expression analysis, I regress expression of thousands of genes (almost normally-distributed, i.e., log expression) simultaneously via multivariate linear regression (multiple $y_i$ per record) on age to remove age from expression.  Using the thousands of new residuals (variables), I now have age removed from the problem, since I may not want to deal with age in other analyses.  
A: The concept of "error propagation" describes the effect of noisy input variables onto a functions output - I learned about this concept in context of sensors and noisy measurements. 
Searching for details, google leads us to a rather comprehensive article about Propagation of uncertainty
