The linter complains because you are redefining the same variable multiple times. Thus replacing the ones in the closure containing it.
Instead of redeclaring it just use it:
private getNextStageStep(currentDisciplineSelected) {
let nextStageStep = '';
if (this.stageForDiscipline(this.currentDisciplineSelected) === 'step 1') {
nextStageStep = 'step 2';
} else if (this.stageForDiscipline(this.currentDisciplineSelected) === 'step 2') {
nextStageStep = 'step 3';
} else if (this.stageForDiscipline(this.currentDisciplineSelected) === 'step 3') {
nextStageStep = 'step 4';
} else if (this.stageForDiscipline(this.currentDisciplineSelected) === 'step 4') {
nextStageStep = 'step 5';
} else if (this.stageForDiscipline(this.currentDisciplineSelected) === 'step 5') {
nextStageStep = 'step 6';
}
return nextStageStep;
}