form of the verb

It depends on the noun for which that is used.

If it is singular it will be lets::::

It is your look that never lets you feel................

I don't like your behaviour and appearance that never let you.....................

In English, the choice of verb tense (the basic tenses are past, present, and future, but there are twelve in all) and verb number (singular or plural) is determined by the sentence subject and context. In your examples, that is a subordinating conjunction that refers back to an absent subject. Without knowing the sentence's subject, it is difficult to determine the proper verb.

The question of let versus lets is more complicated than Rahul suggests. Let, meaning to allow, takes the same form for both present and past tenses. It also takes the same form for the singular and plural.

Present -- "I let you paint" "You let him paint" "We let you paint" "They let you paint"

Past -- "I let you paint" "You let him paint" "We let you paint" "They let you paint"

Verbs also express mood -- indicative, subjunctive, and imperative -- and here is where lets enters the picture. An indicative verb states a fact, while a subjunctive verb is used for stating possibilities, conjectures, "what if," or what someone else said, thought or believed. In either mood, let is used as I listed above for both present and past tenses and for both singular and plural EXCEPT with he and she. The indicative present is "he lets" while the subjunctive present is "he let". The indicative past is "he let" as is the subjunctive past.